A Study of Heterogeneous Nucleation in Aqueous Solutions
C. B.Richardson* and Tamara D. Snyder
Physics Department, University of Arkamas, Fayetteville, Arkansas 72701
Received January 18, 1994. In Final Form: April 19,1994@
Single,microscopic,aqueoue solutiondropleta of NaC1, CeCl, KF,andNaNOsare levitated in a quadruple
trap filled with water vapor a t room tem ature. The aolutione become euperaaturated as the preesure
of the vapor is slowly reduced until soli&tion
occurs. Both homogeneous dmpleta and those conelatiq
of a solution jacket surrounding a eolid core of a similar salt, KC1 for the f i a t three, NaBO4 for the last,
are studied. Except for KF,the solid catalyzes the nucleation, reducing the maximum supersaturation
to 48, 78, and 64% of ita value in the absence of the eolid for the other three, reepectively. Classical
nucleation theory yielda the &tical size of the nucleus, ita surface energy deneity, and, assuming it is a
spherical cap on the aurface of the solid core, the wetting angle.
I. Introduction
Solids in contact with metastable liquids may catalyze
the liquid to solid transitions1 I t is generally believed
that the transition i s opposed by the free energy increase
which accompanies the formation of the eurface of the
embryo solid within the liquid.* Contact between that
surface and a catalyet reduces the energy and the limit
of metastability.
To obtain valid results when studying the transitions,
it is necedsary that the liquid be pure and the surface
clean. Cleaving a solid may produce euch a surfaces8I n
this paper we report the results of experiments in which
the metastable liauid is a supersaturated solution and
the clean surface ie produced Gy precipitation of a eolute.
A second solute remaim completely dissolved in a solution
nucleation
which is elowly made more e~&-~a-turateduntil
occurs.
The sample is a microscopic droplet, charged and then
levitated in a quadrupole trap a t room temperature. The
droplet is in thermodynamic equilibrium with watar vapor
~
which fills the trapand whose pressure is varied t a control
rnetaetabilit~.~
In eectionk we describe the technique, and in section
I11 we present the classical nucleation theorv of Volmefl
and of h b u l l and Vonnegut." In section we present
our resulte, and in section V we conclude the paper.
~
Lt. The Experiment
The aolutione to be etudied are prepared by mixing meaeured
volumee of eaturatedeolutiom of two salts and then dilutingthe
mixture about SO-fold. Reagent grade salta without further
purification and HPLC grade water are used. Charged droplets
of the mixed eolution, roughly 10 pm in diameter, are iqjected
into a quadrupole trap, whoee deeign and operation have been
deecribed previouslyS7A single particle is trapped. The syetem
housing the trap ie evacuated,drying the particle which becomee
a eolid. The eyetern ia then sealed and held at 25 k 0.05 O C .
Water vapor is admitted by opening a valve to a nearby pool of
water. The temperature of the pool ie elowly cycled, Rret
A W a c t publimhed in Advance ACS Abstmctn, June 1,1994.
(l)Vonnegut,B. J. Colbid Sci. lW,3,663.
(2) For a kinetic theorg not wing embryo free energy, rree: Chlang,
P, P.; Donohue, M.D.; Katz, J. L. 3. Colloid Znhrface Sci.1086,122,
261.
(3) Dunning, W.J.; Fox, P. G.; Parker,D. W. In Cryrid Growth,
Pelaer, H. 8., Ed.; Pergamon b r a : Oxford. 1987.
(4) Snyder, T. D.; Riehardaon, C. B. kngmuir 1888,9,843.
(6) Sipbee, I?. A. In N u c k d b n , Zettlemoyer, A. C., Ed.; Msrcel
Dekker, Inc.; New York, 1969.
(8) Turnbull D.; Vonn ,t B. Znd. Eg. C k m . 18(19,U, 1242.
(7) m&n,
C. B.; urtz, C. A. J . Am. Chem. Sac. 1984,106,
@
6615.
y
C
Figure 1. Spherical cap model of the nucleus: C = catalyst,
S = solid, L = liquid.
diseolving one salt and then the second, then precipitating the
eecond, and finally nucleating the solidification of the first.
Though the particle is microscopic with a high surface-tovolume ratio and thua is quick to respond to changing presewe
of the water vapor, the eyetemhae a surface area about 12orders
of magnitude greater and thua ie slow to reepond. To maintain
equilibrium, the cycle time ia typically 1h or more. To reduce
the labor of data wllection, the experiment is partially automated.Ufeedback loop using a CCD camerato view the particle
is used to wntinuouely match ita changingweight with a vertical
electric force. The value of the potential needed to produce this
force and the temperature of the water eourcecomprisethe data.
The levitation technique is an example of 'containerless
proces~ing"
which is advantageousfor nucleation studiee. Since
the eampleie microscopic, undissolved impurities are eliminated
from moat particles. They are unbuched except by vapor and
thus phpically unperturbed, and chemically uncontaminated
above the levele achieved by high-vacuum practice.
III. Heterogeneourr Nucleation Theory
Since our experiment is macroscopic and thennodynamic, we will diecues only classical nucleation theory
here, which is similarly limited. In this theorybulk matter
properties such ae density, surface tension, and free energy
of condensation are assumed for the embryo eolid, which,
ae we shall see, contains fewer than 200 molecules.
Volmefl considered a model in which the embryo sits
on a flat surface of a solid, the potential catalyst. The top
surface of the embryo, in contact with the eolution, is
spherical, with radius r. See Figure 1. We denote the
catalyst, solid, and liquid as C, S, and L. The contact
angle 8 which minimizes free energy is given by
COB
e = QCL
- ocs =
(1)
"SL
where the ds are the interface energy densities. The
change in fiee energy with the production of the embryo
61994 American Chemical Society
A Study of the Nucleation of the Solution-to-SolidPhaee
Transition Ueing Levitated Microscopic Particlee
Tamara D.Snyder and C. B. Richardson*
Physics Department, University of Arkcr~crs,Fayettevilk, Arkansas 72701
Received June 8,1992. In Final Form: October 6,1992
The solution-to-did phase transition Q studied for eightsystem at t = 26 "C, includingsodium bromide
and ~otassiumchloride solutes with Dute and mixed water eolventa and methvl alcohoL Ths nainr11mare
mi~mcopicdroplets levitated in a abdruwle trap which b flllsdwith solve& vawr from a midliudd
source. Withinixperimentd error-the s$emtUration of the solutionr at the timition in the
for
all svstemr: 8' = 3.6 f 0.2. With a nucleation rate wtimated ta be 108 cmd 8-I claeeical nuclmtion theow
yielh 83 for the number of molecules in the critical nuclew for both salts, and surface e n e G de~&G&
of 61 and 46 erg c m - 2 for NaBr and KCI, respectively, independent of solution.
I. Introduotion
The nucleation phenomenon by which matter changes
phase occun on a e d e of length and time which places
it beyond the realm of direct measurement. Clustern of
ten to hundredn of molecules existing for l(rl"lO-8 s
compriw the new phase in coexistence with the old.
E.perimentadetectthe new phase followingagrowth stage
of duration 104 s or more in whIch ita volume incream
10 ordern of mannitude or more.
Theae sx&enta
we a variety of techniques to study
the vapor-liquid, liquid-solid, and solid-solid traasitioas.'
From them and various nucleation theories a general
understanding of the phenomenon has emerged. At
prssent though there have been relatively few studies of
the nucleation of solid phawe, and for those from solutiom
Adamon suggeata2'Supamturation phenomena in s e
lutions, are, of course, very important, but, unfortunately,
data in thisfield tend to be not tooreliablew.In this paper
we report the resulta of meaeurementa of the eolutionbeolid phaw transition for the ealta KC1 and NaBr. In
them the samples are single, micrometer-ahad particlea
levitated ele~trodynamically.~Thie technique has advantages and disadvantages when compared to the classic
cloud chamber technique4or the matrix isolation using
emulrioneP Thew techniques produce eneembles of
noninteractingor e~entiallyc l a d system and thusyield
enurmble averagesfor comparisonwiththeory. The single
particle, though it may be cycled many times, yields far
1- information in practical times. The supmaturation
obtained in the expaneion cloud chamber ie transient,
complicnting the annlysii somewhat. That achieved in
the *ion
cloud chamber han a gradient,and knowledge
of heat andmaw trader is required. Here the micmcopic
solution droplet is in thermodynamic equilibrium with
the eolvent vapor as the droplet pasees elowly through
metantable steta of incmaeiq supmturation.B In the
emuleiomthe solutionsare in contactwith an inert matrix,
for example, eilicone oil, while here the solution in
surrounded by ita vapor with the partial pressure of other
vapors, principally argon, reduced 8 ordern of magnitude
or more. The particles are small and thue 1- likely to
(1)ibttl~moy~.L
C.,Ed.Nucl~tion;MueslDakker,Inc.:
NewYork,
1888.
(2) Ad.mrc31, A. W . Phx~icalChemutry of Surfacr~,5th ed.; John
W h y a d Son4 Inc.: N w York, 1990.
(3)W w r h ,R. F.; Shsltoa,H.;hngmuir, R V. J. Appl. P h y ~1969,
.
-
- --.
30
. IUZ
-,
(4) Andemn,R. J.;MUer,R C.;Kumer,J. L.;Hagan,D. E. J. Atmoc.
sci. 1#)0,87,2608. h t r , J. L.J. Chrm. Phy8.1870,62,4798.
(6) Tklnxmk, P.Ph
lMS, 898,6802.
9;Rev.
a m , J. F.J. ~ e m r o sl i . IM,H,688.
(6) m w a , C.
I.
contain impurities which can catalyze nucleation. But
small particlea require a high nucleation rate for practical
induction timm, and thue the measurements cannot be
made over a range of supereaturations.
In section II we pteeent a brief review of nucleation
theory, and ia d o n 111 we describe the levitation
technique. .Insection IV we pro8nt our readta, and in
section V we dkcuaa and compare them with those from
related studiw, and conclude the paper.
11. Nuoleation Theory
What ia commonly celled cleeeical nucleation theory?
which we will call the standad model, yields a nucleation
rate
where AG* L the maximumfree energybarrier to t r d t i o n
tothe more stable phaae. The system makesthetramition
by fluctuations in composition. In the standard model
the stable phase conebta of spherical clueters of uniform
density equal to the bulk density, and
Here r in the cluster radius, a the surface free energy
density, p the number density of the cluster, and s the
memure of the departure of the ayetam from equilibrium
coexistence, the superaaturation. If the cluetar grows by
fluctuation until
then the barrier reaches a malrimum
--
AG* = AG*(surface)/3= AC*(volume)/2
(16u/3)t?(pk~ln re)-'
(PkT ln 8312
(4)
where i* is the number of molecules in the cluster, the
c r i t i d nucleus.
The 'kinetic prefactorwfor the vapo~to-liquidtraneition
is
where m L t h e mane of the molecule, n b the number
densityinthevapor phase, and q isthe stickingcoeffident.
(7)h & d ,
J . E. Am. J. Phyr. 1W,SO,870; 1W. 91,al.
0743-7483/D8/U09-0347W$0400/0Q 1993 American Chemical Society
through a surface oxide layer on copper. These correspond
to gold plating the contact surface or to roughening it by
coarse sandpaper, as in our case.
'If the actual thcrmal resistancc at low temperatures is about five t i m s
larger than theone calculated from the Wiedemann-Frana lnw as reported
by K.Glocs, P. Smcibidl, C. Kennedy, A. Singsaas, P. Sckowski, R.M.
Mueller, and D.Yobcll, [J. Low Tcmp. I'hys. 73, 101 (1988)], the temperature difference should increa..e t o 3 ILKat T = 30 pK.
'M. Suomi, A. C. Anderson, ant1 B. Holmstrom, I'hysica 38, 67 ( 1968).
.'R.I. Houghton, M. R. Brubt~ker,and K.I. Sanvinski, Rev. Sci. Instrum.
38, 1177 (19671.
'K. Muething, G. G.Ihns, and J. Landnu, Rcv. Sci. Instrum. 48, 1106
(1977).
'M. Manninen .and W. Zimmerman~~,
Jr., Rev. Sci. Instrum. 428, 1710
( 1977).
%. M. Lau and W. Zimmetmann, Jr., Rev. Sci. Instrum. 50,254 ( 1979).
'M.Deutsh. Cryogenics 19.273 (1979).
"'I.Mamiya, H. Yano, "I. Uchiyama, S. Inoue, and Y. Miura, Rcv. Sci.
Instrum. 59, 1428 ( 1988).
Y h c disks were machincd from a commercial g a d c copper (99.8% pure)
and annealed at 950 'C for three days urider oxygen gns Bow (1.4X 10
Tort).. A 1-mm-diam coppcr wire made from the samc lot as thc disks
showed the RRR of4000 after the same heat treatmnent.
'"Model KHY 18, SIEMENS AG, Bcreich Bauelcmente, Ualmstrasse 73,
Postfach 801709, D-8000, Miinchen 80, Wmt Germany.
"NCF-3000and ECF-66 noncyanide gold plating solutions, Nippon Engelhald Corp., 2-4-1 IIamamatsucho, Minato-ku, Tokyo 106, Japan.
"K.Gbos era/.(Ref.1 ).
"Silver adhesive No. 4817, E.I. du Pont de Ncmours and Company, 1007
Market Street, Wilrnington. DE 19898.
'"'Tanaka Kikinmku Kougyou K.K., 2-6-6 Nihonbnshi-kayaba-cho Chuoku, Tokyo 103. Japan.
'"
A stabilizer for single microscopic particles in a quadrupole trap
C.8. Richardson
Physics Department. UniuersityofArkartros,Fuyettevillr,Arkunsus 72701
(Received 10 November 1989;accepted for publication 4 December 1989)
Light scattered from a single particle suspended in a quadrupole trap is focused on the detector
array in a charged coupled diode (CCD ) camera. The video signals obtained from two successive
rows of sensors framing the center of the image are compared and the difference used to control a
superposed vertical field, holding the particle at trap center. The system is effective for liquid and
solid particles in the size range from 1 to IOpm trapped in vacuum or vapor.
Thequadrupole trap, introduced by Srraubcl' in 1956, is
widely used in coridensed matter studies on microscopic
samples.' Because of the relatively small specific charge of
the particle, its motion is significantly affected by gravity. In
order to maintain particle position at, or orbiting about, trap
center it is Ileccssary to supcrposc a static, vertical, dipole
field. Since particle specif c charge commonly changes over
the course of a study, it is necessary to vary the field and
desirable to do this continuoudy by some servomechanism.
Two systems for achieving balance have bee11 described.
In the firs? a particle image is formed tlnd split, with ihc two
parts illuminating two detcctors. Their outputs are compared to produce an error signal to control the vertical field.
In the second" the particle, a liquid droplet of radius greater
than 70 pm, is back lit and the shadow image fills on a
vidicon tube. From the video signal the top edge of the image
is locr~tedto control the vertical field and thc left arid right
edges to determine particle size. Relative arrd absolute
masses are measured with uncertainties of 0.1 and 5%, respective]y.
We have constructed a system using a charge coupled
diode (CCD) video camera to stabilize liquid droplets of
1334
Rev. Scl. Instrum. 61 (4), Aprll1990
radius down to 1p m and solid particles of comparable volume. The system works well for particles whose motion is
damped by a surrounding gas and for those trapped in vacuum.
The scheme is as follows. A particle is trapped and illuminated by an unfocused beam from a helium ncon laser.
Light scattered roughly 90" is received by a zoom lens system
and focused on the CCD array in the camera. Observing the
image on the monitor, the operator manually adjusts the
dipole field to balance gravity and center the particle. The
camera is moved vertically to center the image between two
rows of sensors chosen to define the null point. The video
signal from these two rows is g a t 4 into a control circuit.
This gated signal consists of two pulses of width about 0.5ps,
height up to I V, and separation 64.5 ps, received 60 times
per s. The two are sent to two peak detectors whose outputs
pass to a comparator. The comparator controls the count
direction of a 10-bit, up-down counter which is incremented
or decremented with the video synch pulse. The counter
state is read by a digital-to-analog converter whose output is
summed with the manually cotrolled dipole field potential,
completing the feedback loop.
0034-6748/90/041334-02$02.W
(c) 1990 American Institute of Physics
1334
Max Dresden's School
For Schoolteachers
Do1tzmann's Constant:
To 'D' or not to 'D'?
Another Reading
of 'Inbreeding'
Correction
52-.L'ht. ctrrrcict rlilnlt
t l t c . J~;I+:I,~III.~~~
t s [[it*l)ul,linfn lr01:
C I ' I ~ * ~ ~ ~ I I > ~ I I ; I.C*~'I,~I.I,(~
t i ) 111 1 h v ~ i t ' \ v S
clrrl.!
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1,111: S S t ' !: S I ~ V ~0I ). (.'~jxltp.
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Val. 22. No. 11, pp.
00W-6981188 13.00+0.00
0 1988 Pergnmon I'ress plc
2587-2591, 1988,
pribjCdin Great Driluin.
EVAPORATION O F AMMONIUM NITRATE PARTICLES
CONTAINING AMMONIUM SULFATE
R. L.HIGHTOWER
and C . B. RICHARDSON
Physics Dep;~rtmcnt,University of Arkansas. Fayetteville, AR 72701, U.S.A
(1:irst rc'c-eiuc'828 Drcrmher 1987 and in jirtaljornt 21 April 1988)
Abstract - Singlc solid particles with initial composition about 80% NH4N0, by number, 20% (NH4),S0,
;Ire lcvitntcd in ;III electric U U ~ ~ ~ T lU r~a Int
~C T = 25°C. Particle mass is measured continuallv over wriods of
lo X h ;IS NI-I, and HNO, evaporate and arc rcmoved. For particles in vacuum the-^^^; erective
presrurc aP(Torr),where a is the stickingcoellicicnt,is mcasurcd to be log (zP)=ZI, any,where x is the
N H 4 N 0 , molc Crecliol~ond (I.. = -3.48 x lo-', a,= -7.17, a , =1.28, o,= -1.67 and a,=2.60 with an
up
-,
,
estimi~lcduncerti~intyin al' or 40% of this value. At x = l this gives, by extrapolation, P=(1.09f 0.44)
x 1 0 - q o r r i f # = I. in good agrcemcnt with that calculated from thermodynamics, P=9.46x 10-"orr.
For pilrticlcs i n wiltcr vapor. at ll~~miditics
bclow the lowest deliquescence point at 62%, the evaporation
rate increases. No mass incrcilsc is dclccted when tllc wnter vapor is introduced. For r.h.>40% the
cvapofiltion ratc is indcpcndcnt of NH,NO, molc fraction ur~tilthat falls below about 0.2. Thc results
suggest that NH; and NO, ions are solvated in an absorbed water layer with thc solvation controlling
cvaporatioo. In o warm nlmospl~erewithout NH, nnd HN0,solid mixcd NO;-SO:- particles would losc
most 01 tl~eirNO; in 1-11, uccordiny to our results.
Key word irldc,.~:Nitric acid, solid solution, water coating erect.
INTRODUCTION
i
,
.
I
Major componcnts of the fine fraction of atmospheric
aerosols are SO:-, NO; and NH; ions. In urban
areas the fraction ranges up to 60% of the total
suspended particulate matter. Together aerosol NHf
and NO; are volatile, yielding gaseous NH3
and HNO,. The lifetime of aerosol NO; is estimated
to be a few days (Seinfeld, 1986). With known free
energies and mixing rules, thermodynamics yields
values of equilibrium partial pressures of H 2 0 , NH3
and HNO, in the presence of aqueous NH,N03
solution droplets, with and without SO:- (Stelson
et ul., 1984; Tang, 1980). Solid dynamics is not known.
In the atmosphere equilibrium does not occur and the
dynamics of exchange belween vapor and aerosol
depends not only on energetics but also on the physics
of transport in both phases (Schwartz and Freiberg,
1981) and on the accommodation or sticking coefficient. Laboratory studies of these systems are needed,
Few such studies have been reported. Appel et al.
(1980) detected aerosol NH,NO, volatility by trapping particles in Teflon filters and passing clean air
over them. They found that about half the NO; was
lost by evaporation. Larson and Taylor (1983) measwed the size change ofNH,NO, solution droplets in
a flowing moist air column from which NH, and
HNO, were stripped. They analyzed their results
using gas phase transport theory and solution thermoand concluded that sticking coefficient was
Richardson and Hightower (1987) measured the
rate of evaporation or a single solid (crystalline)
N H 4 N ~particles
3
levitated in vacuum. A small stic-
king coefficient was required to explain their results.
Tang et al. (1981) have reported deliquescence of a
mixed NO;, SO:-, NH: particle but did not measure
evaporation. We know of no study of mixed
NO;SO:particle evaporation.
We have levitated solid mixed particles in vacuum
and in water vapor at pressures below the deliquescence point and have measured loss of mass by the
gravity-balance method(Davisond Ray, 1980)as NH,
and HNO, evaporate. Subsequent light scattering
measurements and simple kinetic theory yield vapor
pressures for the dry and water-coated particles for
NH4N03 mole fraction ranging from zero to about
0.8. Interesting surface and bulk effects are revealed.
The dynamics of these particles in the atmosphere is
discussed.
METHOD
The single-particle levitation scheme used here is
the same as that used in the NH,NOl study (Richardson and Hightower, 1987), The experimental procedure is as follows. Saturated solutions of N H ~ N O J
and (NH,),SO, (ACS grade) are prepared. Equal
volumes of each are mixed then diluted about lo-fold
with distilled water. This sample is loaded into our
particle gun and charged droplets are shot into thc
powered quadrupole trap. Dry air in the trap causes
rapid evaporation of the water. All but one particle are
dropped, the system is sealed and evacuated to a
pressure below loF5Torr in about 5 min. The particle,
illuminated by laser light, is centered by manual
adjustment of the gravity-balancing electric field. As
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/[
On the st;abilit,ylimit of chltrgttd droplets
1
(C!ommuni&~d bg Sir J u m Lighlhill,
~
F.11.S. - Iteemivd 25 July iIQSR)
Single, highly chargod droplotsr of dioatylphthalate and sulphuric arid of
racliuu between 1 snd 10 pm are suapandd in vacuum in a qundrupole
trap. ABLhe rlroplcts uvapornte their radiue is monit>odcontinuo~islyby
light se,ztteriag and their charge in debmined periodically by wwoight
balancing Tlie droplets break when Lhe electric utrens e x m h that of
surft~cu ~tmuion. The lergmt frqmenC mmnins trapped allowing 8
d~t~ermination
of the h g e hl volume and ohargo, Tha frar,tion of
volunte anti chaqe lost is found to be independent of particle size and
mgri of chttrgo and in variable. The oil d r o p low (15.0_+3.9)%of their
charge on breakup UII~
(2.26f0.98) % of thcir m u . The mid rl~vpletu
loso (49.4 & 8.3)% of tl~eirehargo and leeti Lhan 0.1 ?A of their m m . Tho
acid multrr art: r~rnpararlwith those from a mociui of field ernimion b d
upon prolate spheroid ddorrnation m d the formation of Taylor (:orbee.
For both oil and acid rlroplet* the fitabilitv liatih ere in tiprneni, wrtti
those pmlicted by Lord Ray Ieigh.
IXTRODIJCTI~N
The ~tabilityof a (:hawed conducting drop u . ~ sconsidered by I m d Rayleigh
( 1 882). Iio analyawl the c*ylindrit~ally
uymmetric normal rndta of onuillatiun of tho
drop. M'lth ehnrge lmtl than a critical value, dependent on droplob sim and aurfnce
tension, the spt~cricelstitqm i n very wt41ble. With charge at Lhc critical value, bho
Rayleigh limit, srnall yudrupole distortions nro unoppomd. We11 above this limit
octupolc itnd higher distortions are unopposed. Ebr Lhe lnttor case Rnyloigh
cu~tcludcd,without relation to his analysis, that 't.11~liquid in t.hrown out in fino
jebn.'
Taylor (1g64) rewnniderd the gstern by examining the stmsm at t,ht drop
surfac~,whioh he anaiysed for large quadruple clefomattion. With Lord
Itaybiyh's mmtnenh about jet8 find evidence provided by 7Rleny (1917) in a
relatd experiment on the form.ation of a jot at the tip of a glyooririe ralumn in a
ohwged oapilfwy, Taylor went beyond the spheroidal npproximation to conaider
n IwoI defor~natianwhich might load to a jot. T h i ~
i~ in Lho for~nof a cone d
aenlivertical anglo 49.B0, tJ~eTaylor cxbno, which produocs a l l h u n d ~~trese.
R~mier-Smithel id (1971) r~imulataie drop a t the Itayloigh limit, tseating the
lic~uitlIW inviscid and [email protected] in their nimulntion tho droplot i
upherirnl but becoming a prolnte sphero~d.Thie allape in lurgely mnintainod until
the axial ratio T O R C ~ cn.
P ~ 2.5,
Taylor cones suddenly form at the ends.
%veral eexprimental studies of the Rayleigh limit have been reportmi.
[ 319 j
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946
OPTICS LETTERS / Vol. 13, No. 11 / November 1988
Measurements of scattering of light from layered microspheres
R, L. Hightower and C. B. Richardson
Physics Department, University of Arkansas, Fayetteville, Arkansas 72701
H.-B. Lin, J. D.Eversole, and A, 1. Campillo
Naval Research Laboratory, Washington. D.C. 20375
Received April 25.1988; accepted July27. 1988
Experimental elastic-scattering characteristicsof layered microspheres are reported. Single particles consisting of
glass cores coated with glycerine are suspended in an evacuated quadrupole trap, and scattered light intensity is
measured at a fixed angle as the glycerine evaporates. The results are compared with those calculated for
concentric spheres using the Mie theory. Excellent agreement is obtained for glycerine layers of thickness less than
700 nm. For thicker layers, differences occur that are attributed to the effect of gravity on particle structure.
Aden and Kerkerl solved the problem of scattering
from a layered sphere, using the Mie-Debye theory.
This system, which includes coated particles, immiscible liquid droplets, and vesicles, presents an interesting departure from the much-studied homogeneous
sphere. Although the solution was given in 1951, to
our knowledge no precision experiment to verify it has
been reported. In this Letter we present the results of
such an experiment.
In this experiment light was scattered from single
glycerine-coated glass microspheres levitated in a
quadrupole trap.2 Because of the glycerine volatility
the coating thickness decreases from as much as 2.5
pm to zero over the period of a measurement, yielding
a rich variation in scattered intensity for comparison
with theory. Also, because the size of the glass microsphere varies from particle to particle, each gives a
unique spectrum.
Hightower and Richardson3 recently illustrated the
response of a layered sphere to an incident plane wave
with computations of scattered light intensity and energy density within and near the particle. They used
the program of Wiscombe4 to evaluate the solution of
Aden and Kerker for the special case of resonant response. Here their results are extended to include the
general case of the present experiment. Excellent
agreement between theory and experiment is obtained
when the glass sphere volume is less than -20% or
more than -60% of the particle volume.
The glass microspheres were obtained from Duke
Scientific. They have a mean radius of 4.0 pm, with a
standard deviation of 0.9 pm. The glass has a density
of 2.4-2.5 g/cm3 and an index of refraction of 1.51.
Pure glycerine has a density of 1.260 a/cm3 at room
tempirature and an index of refractionbf 1.473. The
glass spheres are supplied dry and are suspended without cleaning in a glycerine-alcohol solution. Particles
of this suspension are shot into the trap and charged
by friction. The chamber is slowly evacuated to a
pressure of a few hundred pascals so that glycerine
evaporation is not diffusion limited.
0146-95921881110946-03$2.00/0
Polarized light from a He-Ne laser is incident upon
the trapped particle. Scattered light is detected by a
photomultiplier tube behind an aperture subtending
0.001 sr, fixed at 90.5' from the exit beam. The photomultiplier tube output is recorded continuously unti1 glycerine evaporation is complete.
.
1
7
Fig. 1.
Record
trace: midway in the
sion), Lower trace:
major division).
with Fig. 2.
O 1988, Optical Society of America
Resonant Mie scattering from a layered sphere
R. L. Hightower and C. B. Richardson
The theory of Aden and Kerker is used to compute the resonant response of large layered spheres to an
incident linearly polarized plane wave. Cases considered include hollow spheres and those with transparent
and absorbing cores whose diameters range from zero up to that of the particle. Both core and layer
resonances are studied. The results are presented as partial wave amplitudes, energy densities, and scattered
light intensities for a typical resonant mode, TE39.
Introduction
The scattering of light from large spheres has been
studied by many researchers. Several reviews of this
work are contained in monog~aphs.'-~Of recent and
special interest are resonances in the sphere-light interaction, discovered by Ashkin and Dziedzic in the
radiation pressure on optically levitated particles4and
detected in a variety of high-resolution experiments
stimulated by this work.5-7 Following this discovery
the theory of the interaction has been carefully reexamineds and found to be in excellent agreement with
experiment.
An interesting variation of the homogeneous-sphere
scattering is that of the layered sphere. This problem
was solved by Aden and Kerker for two concentric
spheres.9 Waitlo has generalized this solution to a
sphere with continuous radial variation of composition, and Bhandarill has considered a similar problem.
Fenn and Oser12and Kattawar and Hood13applied the
Aden-Kerker results to water-coated carbon particles.
Toon and Ackerman14have presented new algorithms
for computing the scattering by reformulating the
Aden-Kerker results to avoid numerical instabilities.
Various perturbation approaches have also been published.ls17 PluchinolB has computed the effect of resonance on the emissivity of an aluminum oxide sphere
coated with a thin carbon layer.
None of these studies presents a comprehensive
treatment of the resonance of a layered sphere, however. In this paper we consider the Aden-Kerker theory
of scattering from concentric spheres at and near reso-
I.
nance for a variety of particles, including a hollow
sphere and spheres with transparent and absorbing
cores. We investigate both the core resonance and the
shell resonance. We present graphically the solution
to the transcendental resonance equation for a representative layered particle and illustrate our results
with plots of partial wave amplitudes, energy densities,
and scattered light intensities vs frequency of the incident wave. Possible applications of these results in
aerosol science are discussed. In a companion paper,
we compare equivalent results with those obtained
experimentally.lg
II.
Theory
A wave polarized in the x direction and of amplitude
Eo, wavenumber k, is incident in the z direction on a
layered sphere with the center at the origin. The core
of the sphere has radius rl and refractive index ml.
The shell has outer radius rz and index nz. The sphere
is surrounded by vacuum. We must determine the
fields in the core, layer, and near zone to determine
energy distribution at resonance, and in the far zone to
determine scattering. Expressions for the former are
given in the Appendix.
The components of the outgoing wave far from the
particle are written in spherical coordinates as
- wt) cos$S,(O),
E, =: (i/kr)Eo expi(kr - wt) sin&SI(O).
E, = (ilkr)E, expi(kr
(la)
(lb)
The scattering functions S~(fl)are expanded as
m
The authors are with University of Arkansas, Physics Department, Fayetkville, Arkansas 72701.
Received 22 January 1988.
0003-6936/88/234850-06$02.00/0.
O 1988 Optical Society of America.
4850
APPLIED OPTICS I Val. 27. No. 23 / 1 December 1988
S2(9) =
1(2n + l)/n(n + l)[a,+,(BI + bnxn(B)l,
(2b)
n=1
where nn(fl) and ~ ~ ( are
8 ) :simply related to the associated Legendre polynomials (see Ref. 1,p. 124). The
partial wave coefficients are given by
Wb(4981/81 O.M+0.W
o u d Ltd.
0 1981per- l
EVAPORATION O F AMMONIUM NITRATE PARTICLES
C. B. RICHARDSON
and R. L. HIOHTOWER
Department of Physics, University of Arkansas, Fayetteville, AR 70701, U.S.A.
(First received 14 April 1986 ond injinol fonn 2 September 1986)
Abstract-Microscopic anhydrous ammonium nitrate particles are levitated in a vacuum in an electric
q ~ a d ~ ptrap
l e at 2YC. S
i
z
e and mass changes of the evaporating particles are monitored continuously in
siru using light scatteringand gravity balancing. Both supersaturated liquid droplets at the zero-solvent limit
torn.
and crystallinesolids are studied. The measurai mpor pressure of the liquid is p = (3.18 ? 0.45) x
dr
Fresh solid particlesevaprate at a r a t e 2 = -0.23 A s- wherer is an equivalentradius. Beyond 4 h the rate
is a constant -0.06 s- '. These rates arc consistent with that predicted from thermodynamics if the mass
accommodation coefficient is a = 0.02 initially and 0.004 after 4 h. Aerosol sampling by several groups
indicates the presence of solid ammonium nitrate particles in the atmosphere. Long lifetime and long-range
transport of these particles are predicted regardless of ammonia and nitric acid vapor concentrations.
".
Key word index: Ammonium nitrate, light scattering, sticking coefficient.
Ammonium nitrate is a common atmospheric aerosol
occurring in both solid and solution form. In contrast
with ammonium sulfate, the nitrate is volatile at
normal temperatures. For solution droplets a complex
exchange of H,O, NH, and HNO, between the vapor
and condensed phases occurs. Thermodynamic analysis (Tang. 1980) p&icts the occurrence of acid particles as a result. A recent review by Stelson et al. (1984)
contains many references to related studies.
Larson and Taylor (1983) have measured the evaporation of ammonium nitrate solution droplets passing through a chamber in which NH, and HNO, are
removed from the ambient vapor. They find good
agreement between their results and thermodynamic
and kinetic theory predictions.
Stelson et al. (1979) have discussed the dynamics
when the particle is solid ammonium nitrate. They
use thermodynamic data and the high-temperature
measurements of dissociation pressure by Brandner et
al. (1962) to conclude that much of the ammonium
nitrate in a volume of air is in the vapor phase as
dissociation product.
We have measured the rate of evaporation of
anhydrous ammonium nitrate particles at 25°C using
the technique of single-particle levitation in an
evacuated quadruple trap (Richardson et al., 1986).
The particles occur in both solid and liquid phases, the
latter unexpected. The results are compared with
thermodynamics and used to discuss particle dynamics
in the atmosphere.
METHOD
The levitation technique has been described elsewhen (Richardson and Kurtz, 1985). A properly
Shaped oscillatory electric field may yield forces which
c o n h e pm-size charged particles to very small volumes for unlimited times. Particle mass-to-charge
ratio may be measured in situ with a precision of 0.1 %.
If the particle is liquid and light is scattered from it,
index of refraction, dependent on composition, may be
measured to about 0.1 % and radius to 10 ppm.
A schematic drawing of the apparatus is shown in
Fig. 1. A quadrupole is housed in a massive temperaturecontrolled vacuum chamber. The chamber
is connected to a 170 d s - turbomolecular pump
through highconductance and precision leak valves in
parallel. It is vented through particulate filters and
Drierite, zeolite and liquid-nitrogencooled traps in
series. An air pump capable of flushing 250 ml s- of
filtered air through the chamber is attached. This
provides a barrier to room air when the top port'is
open.
'
'
Fig. 1. Schematic diagram of the apparatus. Q
= quadruple
trap; L = HeNe laser; TC
= temperature controller; TMP = turbomolecular
pump; MP = mechanical pump V1- p h i o n valve;
V2 = highconductance valve; V 3 = vent valve; C
= liquid nitrogen trap; Z = zeolite trap; D = Drierite
column; AP = air pump.
Growth Rate Measurements for Single Suspended
Droplets Using the Optical Resonance Method
C . B. Richardson
Physics Department, University of Arkansas, Fayetteuille, AR 72701
H.-B. Lin, R. McGraw, and I. N.Tang*
Department of Applied Science, Brookhaven National Laboratory, Upton, NY 11973
An experimental technique described with which the
growth rate of a single solution droplet by water vapor
condensation can be repeatedly measured with high precision. The technique involves the use of an electrodynamic cell to suspend a NaCl solution droplet in
water vapor and a CO, laser to momentarily perturb the
droplet-vapor equilibrium. The droplet size change dur-
The application of single particle levitation
techniques has made it possible to study
many interesting and important processes associated with aerosols. A recent review by
Davis (1983) on transport phenomena with
single aerosol particles serves as an excellent
reference to both experimental techniques
and aerosol transport theories. More recently, Tang and Munkelwitz (1984) have
studied crystal nucleation from aqueous electrolyte solutions by determining the critical
supersaturation at which a suspended solution droplet transforms into a salt crystal.
Richardson and Spann (1984) have measured
t h e water cycle in ammonium sulfate. Kurtz
a n d Richardson (1984), have detected
solid-solid, solid-liquid, and liquid-solid
phase transitions in the lithium iodide-water
system. Richardson and Kurtz (1984) have
described a novel isopiestic measurement of
w a t e r activity in lithium halide solutions.
*Correspondence should be directed to I. N. Tang.
Aerosol Science and Technology 5:103-112 (1986)
ing condensational growth is monitored with a tunable
dye laser for a particular optical resonance due to Mie
aattering. A consideration of the coupled heat and mass
transfer processes during droplet growth indicates that
the best agreement between theory and the experimental
results is obtained with a condensation coefficient close
to unity.
Spann and Richardson (1985) have studied
ammonium acid sulfate systems.
We report here an experimental technique
with which the growth rate of a salt solution
droplet by water vapor condensation can be
repeatedly measured with high precision. The
technique utilizes a tunable dye laser to generate a set of time-resolved optical resonances for solution droplet undergoing condensational growth. Since for a given resonance the ratio of the particle radius, r, to
the resonant wavelength, A, remains constant, the experimental particle size resolution, Ar/r, is determined by the dye-laser
linewidth, AA/X (Ashkin and Dziedzic,
1977). Consequently, a size resolution of 1
part in
6000 is easily achievable with a
co~mercialdye laser having a bandwidth of
1 A in the visible region. Such size resolutions allow detection of "monolayer deposition" on a micrometer-size particle.
In the present study, the technique is illustrated with an NaCl solution droplet initially in equilibrium with water vapor at
ambient temperature. The equilibrium is
slightly perturbed by momentarily irradiat-
-
Optical measurement of the evaporation of
sulfuric acid droplets
C. B. Richardson, R. L. Hightower, and A. L. Pigg
Single micron-size sulfuric acid droplets are levitated in vacuum in a quadrupole trap through which passes
the beam from a He-Ne laser. Scattered light is monitored by a fixed detector as cavity resonances are
excited in the evaporatingdroplet. Me-Debye theory is used to determine particle size, which, with kinetic
theory, yields vapor pressure. Over the temperature range studied, -10 to +30°C, the vapor pressureof pure
sulfuric acid is Inp(Torr) = (20.70 f 1.74) - (9360 f 499)/T(K).
I.
Introduction
The scattering of light from microscopic spheres can
yield their size when the results are analyzed using
Mie-Debye
High precision is possible if the
light excites cavity resonances in the spheres. These
resonances were discovered by Ashkin and Dziedzic in
They have been detected in fluooptical le~itation.~
rescence5 and elastic6 and Raman ~cattering.~
Ashkin and Dziedzic6 have discussed the utility of
resonant light scattering for the measurement of particle evaporation. A fixed frequency source may be
used to determine the radius with a precision of 10ppm
as a'micron size evaporating droplet passes through
resonances.
We have levitated single, charged droplets of sulfuric acid in vacuum in a quadrupole traps and measured
their rate of evaporation by monitoring the intensity of
light scattered 90". The vapor pressure of the pure
liquid is thus determined for temperatures between
-10 and f 30°C.
Sulfuric acid is a significant part of the particulate
matter in the earth's atmosphere. The rate of formation of liquid droplets by vapor phase condensation
and the lifetime of the droplets are dependent on the
liquid vapor pressure. Although the literature on sulfuric acid thermodynamics is extensive, vapor pressure
measurements are few and in general are made on
aqueous solutions for which acid pressures are l0w.9
Gmitro and Vermeulenlo have calculated the partial
pressures of HzO, SOa, and HzS04 above the solutions
The authors are with University of Arkansas, Physics Department, Fayetteville, Arkansas 72701.
Received 28 October 1985.
0003-6935I861071226-04$02.00/0.
O 1986 Optical Society of America.
1226
APPLIED OPTICS / Vol. 25, No. 7 1 1 Aprll 1986
for compositions between 10 and 100% acid and for
temperatures between -50 and 400°C using the thermodynamic data of Giaque et al.ll Verhoff and Bancherognoted the sensitivity of the results to changes in
input values. For example, a 0.3% change in the heat
of formation of the acid leads to an 81%change in vapor
pressure.
Two recent measurements have been made on concentrated solutions. Roedel12 monitored the transfer
.of radioactive 35Satoms between acid pools a t 95-97%
concentration and room temperature. His best value
for "pure (99%)"acid at 23OC is p(Torr) = (2.5-as+1.3)
X
-10 times less than that calculated by Gmitro
and Vermeulen. Ayers et aZ.l3 transferred the vapor
over a pool of 98%acid to an alkali detector. Between
T = 338 and 445 K they find Inp(atm) = 16.259 10,156/T(K) for 99% acid, giving by extrapolation
p(Torr) = 0.99 X
at 23OC, in fair agreement with
the Roedel value.
The results reported here are the first for supercooled acid and the first over a wide range of temperatures around normal..
II. Experiment
A.
Apparatus
A schematic drawing of the experimental arrangement is shown in Fig. 1. The major parts of the apparatus are a quadrupole trap of Wuerker designsJ4 for
particle levitation, a massive temperature-controlled
vacuum chamber housing the trap, a turbomolecular
pump for production of high vacuum, a 5-mW He-Ne
laser light source, and a photomultiplier detector.
The design and operating parameters of the trap have
been presented elsewhere.16
TMS Annual Meeting 123
(9:00 a.m.)
ON MlCRDGRAVlTY SIMULATION BY NEUTRAL BUOYANCY TECHNIQUE,
-1. Heseguer and A. Senz, Laboratorio de Aetodlt~Bmlca, E.T.S.I.
Aerankutlcos. Univeraidad Polltbcnica. 280PO Wadrid. Spain.
the study of llquids in microgravity c o n d l r i o n ~appears aa a
very promising field owing to the large num?er o f applicatlona
in space technology. The expenaes and difficulty involved in
performing space experiments Is one of the reasons to develop
experlmertal support on Earth. The uae of neutral buoyancy
technique offers to s;lentiste a cheap. ahort time preparatlon
medlum for experlmentatlon with i n t e r f a c e 6 in 8 i m u l a t e d
microgravity. Concerning axLsymetrlc interfecea. thin technique
has been used for a long tlme for static procesees end recencly
lome successful attempts have been made in connection with the
dynamics of liquid bridgea. In thin paper the maln effects on
the dynamics of a liquid tridge due to the presence of an outer
l:quid, as occur. in e x p e r i m e n t 8 using the P l a t e a u - t a n k
trchnique. are considered. In addition, t h e I n f l u e n c e o f
experimental boundary conditlonn is discussed.
(+:25 d.m.1
UEASUREHENT OF PHYSICAL PROPERTIES OF HATERIALS U S r K ACOUSTIC
LCVIT4TION*: E.H.Trcnh. Jet Propuleion Laboratory, Pasadena, CA.
'licrogravity conditions allow the processing of materials ir a
crntainerlers manner through acoustic for other) positionlng
and mantpulatiou techniques. The interaction of the acoustic
radiation pressure with the l l q u l d and solid samplea also allows
the measurement of ~ e r t a i nproperties of the materials under
scrutiny. m e density, surface tension, viscoaity. index of refraction. and compressibility can be measured using sarnplca
With srze ranging from I cm down to 500 micramererr. An impartant application lies in the determination of the properties of
substantially undercooled l~quids.
------------------
electrodynmically i,. vacuum in a quadrupole trap
W d e r vapor id
slovly introduced causing theparticle to undergo se4oential cryatalline phase changes to the hydrated solids L11-nH 0 vith n
1.
513. 2. 3 . The pressure at each change !e measured! The vapor i s
s1,wly removed a.?d changes to n
2. 1. 0 occur at which the pressure is meaeurej. Hysteresis occurs. The results are analyzed
,lain% simple nuclearion theory to determine the free energy barrier to the trersitions. The transition from LiIa3H 0 to satursLed Eolution is also studied. The reaults suggest fhe elistence
of an internediere solid state conslstfng of water molecules a b
sorted between the graphite-like crystalline la:.ers.
'Work supported by NSF. **Present address: Argonnr tiation~l
Laboratory.
-
-
(1::-5
*..?.I
-
THE P!f?OGRCiVITV WATERIALS SCIENCE LABORAlORY AN OPPORTUH~TY:
L. r . Greentauer Sen
NASA Lewis Research Center. Clevelan5.
~~r&'~ateric~s
Science Laboratory (HMSL) is a
nbtjonaily available facility located at the NASA Lewis Research
Cef.ter. The MMSL Is open to scientists from indestry. university. and govern,wnt organizations to study and develop their
m f c m ~ r a v i t ymaterials science exprrimstal ideas. Visiting
scientists may conduct expertmots as precursors to the use of
ground-based reduced gravity facilities or in prevaratio~ to
pualify a materials science experiment for a Space Shuttle
flight. The
contains functional duplicates of Shuttle
flight hardware for research at one-g; the first step toward
understandi~y the affects on materials an0 processirq phenomena
at low gravity. Initially metal and alloy solidification a ~ d
crystal growth research w111 be supported, however, ,.*uipmert
required for microgravity-related research m glasse:. cerdmics.
and polymers will soon b? added. Exte~sivesatdriais characterlzation laboratories and advarced computational capabilities
are also available to support the research. A description of
the experimental cao~billtiesprovided in the NMSL and the
process for application will be presented.
work supported by NASA
(11:50
;9:50 a.m.)
7NE EFFECTS OF GRAVITY LEVEL DURING UIRECTIONAL SOLIDIFIWTloN
C:l ME HtCROSTRUCTURE OF Al-In-Sn ALLOYS: **P.A. Currert
'W.F. Kaukler, and **M.H. Johndtan **NAS:JPISFC
*The ~ni;ersit~
of Alabama in Huntsville. 0epattmAt of ~he~nicaiEnsheering
a-IaIn-xSn. ( x
0.6,11,22).
elightly hypermonotectic alloys
were directionally solidifid during aircrart low-gravity
(1ow-g) maneuver6 eacn consisting of about 25 seconds of
low-g ( 1 0 ~ ~ 8-ad
3
1 ainute of high-g 0.5g).
TypIcal!y, several
millimeters of sample was solidified in each low-g period.
Cslculatioms and w r k with transparent metal model materiels
l n d i ~ a t echat convective and Stokes flows are damped by a factor
of 100 within 4 seconds in low-g. Sample composition and microstructure vere correlated with accelerometer data, For the 6
and 14 vt.X Sn alloys mvelopmsnt of I.. phase by the solidifieation front and for the 22 w t . 2 Sn alloy the alllpment and
shape of the ~ n - ~rich
n phase appeared to be a functiry of
the gravity level during .solidification.
-
110:15 a.m.)
BREAK
110:35 a . m . )
A COHPARISON OP D~RECTIONALSOLIDIFICATION 1N A m m T I C FIELD
AND UNDER MlCROGRAVITY CONOlTlONS AS A WEANS OP CONTROUZNG
NICK~LBASE SUPEULLOY HICROSTRUCTURES: W . S . Alter*. J.B.
*ndre~-t, M.H.
Johnston*. P.A. Curreria, W.O. Hamilton'.
'NASA
Marshall Space Plight Center, Huntsville, AL 35812,
TUniserstty of Alabama at Birmingham, Birmingham. AL 35294
Variation8 In carbide morphology and v o l m e fraction are often
found In dlrecci.1nally salidified aupecalloye and are thought
to have a significant influence on the aervlce life of
components. Recent research has iadicated that directional
eolidific.stlon unde. microgravity coniitiona can affect the
she.'?
and v o l m e fractiun of the carbide phase in these alloys.
presmebly due to the reduction of gravity :nducrd flovs such
as convection. In thia study, e magnetic field was utilized to
dampen fluid flov during ground based directional solldification experhents. A comparison has been made berueelk the
carbide morphologiee and v-iume tractlona In IU\RU 24b superalloym direetionsllv solidi! led under a magnetic Cleld and
under microgravity conlltlons.
q o r k has been s u ~ p o r r ~ h t h r o u ~ ' h 7 h ~ r eSpace
h a l l Flight
center mterlala and P I O C ~ S S ~LSs ' J o r ~ t o r ~
111:00 a . m . )
HEASURDIENT OF PHASE CHANCES IN A LEVITATED LITHlIRl 1ODIi)E
PARTICLE*. C. b. Richardson and C. A. Kurtzb*. Physics Depsrtment. University of Arkansas, Fayetteville. AK 72701
A charged micron-size particle of lithium iodide is scspended
z.n.)
tLtC19ONIGNEIIC CONIAIHCRLLSS PGDCLSSING: EM1 Shultle Apparatus and
fxDrrlmenrs
RoL,ert 1. Frost. General Llectrtc to. Soace Dlvirion, valley Forge.
Kinq of Prurrla. PA.
Phe dDpdVatuS. recently rebuilt and quallrled for melttnq and
s0lidiftcatton erperimrntr in :.,e ortiter cargo Ddl lr described. as
well as the status of the Init.al scrier of plannro P.D~rlments
usinq the facllrtv and p:snrwd ~a~lfirations.The prewnt device
uttlices high power RF induction meltinq. lollowed by nearly zera
power eiectrornaqnetir yosit~onlng. A soecimta e%cnrnqer. pyromter
dnd movie camera are provided for obscrvntion of sequential
speiimen~during melting or cb~rlngtubscquent undercooling and
rCcaleste~.ce. Cd~abilitieSwill be described as well 4s a brief
Iuranary of the on-going experiments.
(sublect to formal GL management approval)
EXPERIMENTA: TFKHNIQUES IN HIGH
TEMPERATU?G. SCIENCE VI
Sponsored by the Thermodynamic Data Committee, Materials
Science Division, American Society for Melal~
Thursday, March 6, 1986
Mardi Gras F.G
8:30 a.m.
Marriott Hotel
Chairn~an:R. A. Schiffman, Midwest Research Institute,
Kansas City, Missouri 641 10
Session Chair: D. R. Olander, Department of Nucle
Engineering, University of California at Berkele
Berkeley.CA 94720
(8:30 a.m.)
DYNIWIC TECHNIQUES FOR HEblSUREUENTS OF THERHOPHYSICAL PROPEXTIES
AT HIGH Tk?+PE!UTURES: A. Cera:rlim.
National Bureau o f
Standards. ~ a t t h e r r b u r - 7
* e c h n l q u e s ere described for the d mamic mea~urementsof selected
thermophysical properties of electrically conduct in^ solids in
the range 1500 K to the melt in^ temperature of the specimen. The
techniques are based on rapid resistive self-heating of the
specinen from room temperature to any desired hieh temperarmre in
less than one second hy the passage of an electrical current
Pulse through it and on measuring the pertinent quantities vith
millisecond resolution. The techniques vere applied to the
measurements of heat capacity. electrical resistivity. hemispherical total emissivity. normal spectral emissivity, thermal
expansion. temperature and energy of solid-solid phase transformations. melting terperature. and heat of fusion. Extvnsion of
the techniques to measurements above the melting temperature of
the specimen are brietly discussed.
" e t c h v t m n r n l Vol 19, No 5. pp 819-825. 1985.
wlcdin Om1 Bnuin.
MEASUREMENT O F THE WATER CYCLE IN MIXED
AMMONIUM ACID SULFATE PARTICLES
J. F.SPANN*
and C.B. RICHARDSON
Physics Department, University of Arkansas, Fayetteville, AR 72701, U.S.A.
10 October 1984)
(First received 9 July 1984 and in~?~l/orm
Abstract-A single ammonium-hydrogen-sulfate particle is levitated in an evacuated quadrupde trap at
room temperature and the temperature of an attached tube containing bulk water is slowly cycled
introducing then removing water vapor. With increasingpressure the particle dissolves in stages, thcn grows
as a solution droplet by watcr absorption. With decreasing pressure the droplet supersaturates,crystallh,
thcn dehydrates completely to return to its initial state. Particle mas$ and thus composition, is measured
continuously with an electrostatic balance. Twenty-six cycleswerestudiedassolutccompositionranged from
ammonium bisulfate through lctovicite to ammonium,sulfatcin roughly equal steps. Composition was
changed in sit u by reaction with ammonia at low partial pressure. With solutccompositionchar~terited
by x
= [NH4]/[S04], dcliqu*rencc was found to oavr at water activity a, = 0.394-0.029 (x - 1) for 1 < x
< 1.5 and a = 0.710-0.023(x- 1.5) for 1.5 < x < Z Particle growth occurs at deliquescence and
subsequently7s in excellent agreement with that predicted in a model proposal by Tmg for dissolution of a
two-component mixed solute. Water activities of the solution droplets am measured up to a, = 0.9. The
results are compared with those predicted by the Zdanovskii-Stokes-Robinson method of interpolation
from binary data md with those obtained using the mixiig ~ l ofc Mcissncr and Kusik. Particle
crystallization from supersaturatedsolution is analyzed thennodynamically using measured water activities,
the Gibbs-Duhem equation, and classical nucleation theory. The s p a i k free energy barrier to crystallization. AG/n, is found to increasefrom near zero to 0.04 tV ascompoaition ranges from x = 1 to 2, where n is
the number of formula units in thecritical nucleus. New phasediagramsare presented and used to discuss the
dynamics of mixed sulfate particles in the atmosphere.
Key word index: Acid sulfate prtidcs.
INTRODUffION
subw atmospheric particla
growth in moist atmospheres of particles of the mixed
"Its (NH4)z Hz-x SO4 with x = 1.00, 1-57, 1.69 and
constructed a room tempera2.00. These authors
ture phase diagram the mixed sulfatwater system
using the solubility data tabulated by Scidell and Linke
(1965), sulfuric acid solution water activity (Robinson
and Stokes, 1959)and thermodynamic reasoning. This
diagram has proven very valuable in analyzing field
are composed primarily
of sulfate and ammonium ions. Christian Junge (1953)
using chemical spot testing of particles collected by a
fractionating impactor conclude,, anemeasurement
at Round Hill (Mass.) thus confirmed once more that
natural aerosol particles below abut
0.8 pm radius
consist almost entirely of SO: - and NH;, a fact which
is pr~bablyvalid the world over". Brosset (1978) measurements.
Ammonia concentrations in the atmosphere and
identified ammonium sulfate, letovicite and ammonium bisulfate in the water-soluble fraction of gas-to-particle conversion rates determine the mixed
particles collected on the s w d i s h west coast. one sulfate particle compositions. Scott and Cattel (1979)
lhe ammonia
pressurc Over
(1978) analyzed fine particles collected on the summit have
o f ~ t~,,,i
.
with the detection of sulfuric acid and anhydrousammonium sulfate. Theiranalysisof results
in mmonia prcssurc with
ammonium sulfate further c o n f i n d Junge's con- predicts a rapid d~~~
elusion. Weiss et al. (1982) have measured with 5-min
in x. BrOsset
has
NH3
pressure over the mixed salt solutions. Much higher
time resolutionthe
of submicron particles
near the shenandoah ~
~ park ~ values are
i found~ than those
~ over~the solids.
l Brosset
has
predict
the
dynamics
of
(Virginia). On average, fifty-eight per a n t of the mass
ammonium-hydrogcnsulfattwater
particles
in
the
was in the two ions with the molar ratio [NH4]/[S04]
requires a more complete phase diagram
ranging between 0.5 and 2.0 with some regularity.
than
that
now
available, including relative humidities
and labratory stud,es of the
sveral
ammon~um-hydrogensu~fattwater
system have a1 which liquid-to-solid phase transitions occur.
We have xnea~ured the water cycle in 26 mixed
been made. Wishaw and Stokes (1954) have measured
ammonium4ydrogen-su1fate
salts ranging in
the water activity of ammonium sulfate solution. Tahg
et d. (1978) have measured the deliquescence and p~sition from pure ammonium bisulfate to pure
ammonium sulfate. Single p s i z e particles are levi*Present addreas: United States Depart-t
of Energy, tated in vacuum. Water vapor is introduced from a
METC, Morgantown, W.V. 26505, U.S.A.
chilled pool, following the example of Stokes (1947).
819
COLL
161.
MEASUREMENT OF THE DELIQUESCENCE, ACTIVITY, AND CRYSTAL NUCLEATION OF THE MIXED
AMMONIUM SULFATE-AMMONIUM BISULFATE-WATER SYSTEM AT ROOM TEMPERATURE. J. F. Spann,
C. B. Richardson, Physics Department, U n i v e r s i t y o f Arkansas, F a y e t t e v i l l e ,
Arkansas 72701
Large amounts o f s u l f a t e compounds i n atmospheric aerosols a r e thought t o r e s u l t
from SO gas emissions o f i n d u s t r i e s which burn coal as a source o f energy. These
aerosol$ o f t e n c o n s i s t o f concentrated s o l u t i o n s o f (NH4)2S04-NH HS04 We have made
thermodynamic measurements o f t h e (NH ) SO NH HSO H 0 system a? room temperature using
. ~ & r ? i c l e , i n i t i a l l y NH HSO , i s
s i n g l e electrodynamical l y suspended p $ r $ i ~ f e s A
suspended i n vacuum and then d i s s o l v e d as t h e pressure o f water vapor a d i i t t j d increases
through t h e deliquescence p o i n t . The p a r t i c l e i s r e c r y s t a l l i z e d and subsequently absorbs
mixed s o l u t i o n , b o t h d i l u t e and supersaturated, w i l l be presented along w i t h a model o f
d i s s o l u t i o n o f t h e mixed c r y s t a l s c o n s i s t e n t w i t h o u r measurements. Free energies o f
d i s s o l u t i o n and c r y s t a l n u c l e a t i o n b a r r i e r s a r e c a l c u l a t e d from o u r measured a c t i v i t i e s .
THURSDAY MORNING
162.
- SECTION E
-
GENERAL
-
S . E. Friberg,
Presiding
AGGREGATION OF HEXADECYLAMMONIUM-4,4,4-TRIFL.UOR0BUTYRATE IN BENZENE. Barbara J
Konieczkc, Department of Chemistry, Purdue University, W. Lafayette, IN 47907
.
Solutions of hexadecylamoniurn-4,4,4-trifluorobutyrate in benzene were studied as a
~
magnetic resofunction of concentration at several temperatures by means of l 9 nuclear
nance spectroscopy. The association of the surfactant was described in terms of a multiple equilibrium model, as well as a single equilibrium model. The distribution of micellar size was obtained as a function of surfactant concentration. It was found that a n
increase in temperature was accompanied by a n increase in the free energy change for
aggregation and a decrease in the apparent aggregation number. The system was also
studied with added amounts of water.
163.
MICELLAR SOLUBILIZATION OF CHOLESTERYL ESTERS BY A NONIONIC SURFACTANT.
Hans Schott, School o f Pharmacy, Temple, U n i v e r s i t y , P h i l a d e l p h i a , PA 191 40 and
F. A. A. Sayeed, Abbott Laboratories, North Chicago, I L 60064.
t
M i c e l l a r s o l u b i l i z a t i o n o f c h o l e s t e r y l s t e a r a t e , o l e a t e , l i n o l e a t e , and 1 i n o l e n a t e
b y t h e nonionic s u r f a c t a n t nonoxynol 1 0 ( I g e p a l CO-710 o f GAF Corp.) was i n v e s t i g a t e d as
a f u n c t i o n o f t e m ~ e r a t u r e . Below t h e me1 t i n 9 ~ o i n t so f t h e e s t e r s . s o l u b i l i z a t i o n
reduced temperatures o f 4% above t h e c r y s t a l 1 i n e me1 t i n g p o i n t s
where
s o l u b i l i z a t i o n decreased by o n l y 12% from c h o l e s t e r y l 1 i n o l e n a t e t o the o l e a t e .
Therefore. the s o l u b i l i z a t i o n l i m i t s o f c h o l e s t e r v l e s t e r s a t anv t e m w r a t u r e d e ~ e n d
( O K ) ,
mI
a
l e s s e r tendency o f polyunsaturated c h o l e s t e r y l e s t e r s t o form a t h e r o s c l e r o t i c plaque.
164.
MICELLAR SOLUBILIZATION OF MIXTURES OF CHOLESTEROL WITH CHOLESTERYL ESTERS AND
WITH LECITHIN. Hans Schott, School o f Pharmacy, Temple U n i v e r s i t y , P h i l a d e l p h i a .
PA. 19140 and F. A. A. Saveed. Abbott L a b o r a t o r i e s . N o r t h Chicaao. I L . 60064.
The sol i d phase i n e q u i l i b r i u m w i t h c h o l e s t e r o l s o l u b i l i z e d i n aqueous mice1 l a r
nonoxynol 10 ( I g e p a l CO-710) s o l u t i o n s was t h e monohydrate (ChMo). I t s l i m i t o f m i c e l l t r
s o l u b i l i z a t i o n increased l i n e a r 1 v w i t h t e m ~ e r a t u r eand n e a r l v t r i ~ l e dbetween 27"and 51 .
rn
about 71% a t 27" and 37% a t 44".
S i m i l a r r e d u c t i o n s r e s u l t e d when t h e s u r f a c t a n t
I. At~rnsolSci.. Vnl. 15. No. 5 , PQ.563-571, 1984.
Printed in Grenl Brilsin.
MEASUREMENT OF THE WATER CYCLE IN A LEVITATED
AMMONIUM SULFATE PARTICLE
C. B. RICHARDSON
and J. F. SPANN
Physics Department, University of Arkansas, Fayetteville, AR 72701, U.S.A.
( F k s t receisrrl 15 December 1983; utid in revi.rrd form 26 Januury 1984)
Abstrnct-Single micron-size nrnmor~iumsulfate particles are suspended electrodynamically in ti
vacuum. Water vapor is slowly ndrnitlcd unlil ddiquescence occurs, then slowly removed until the
solution droplet crystallizes. Deliquescence isshown to occur through thrce-phaseequilibrium stntes.
During dchydrntion thc vupor prcssure of the supersaturated solution is measured. Thc results arc
compared with a recent theory o f uqueous clcctrolytcs exlrapolatcd to the very high concentrations
encountered and used w i ~ hsimple nucleation theory to estimate the magnitude of the free-energy
bilrrier to crystallihtion.
INTRODUCTION
A charged particle in an inhomogeneous electric field which oscillates symmetrically in time
seeks a point of zero field and may therefore be trapped with electric forccs alone. A great
variety oftraps based on this principle (Paul and Raether, 1955)have been reported. Most use
electrodes with cylindrical symmetry to produce a lield with the null-point centered. Thc
simplest ol' these was that of Straubel (1956) consisting only of a wire ring driven at high
voltage. Charged microscopic particles are trapped in the center. Other noteworthy traps
include the parallel flat discs of Straubel(1959),andthesphere-tubearrangement of Berg and
Gaukler (1 969). Interesting non-cylindrical traps are thecube of Wuerker er ul. (1959)and the
'racetrack' of Church (1969).
An even greater variety ofexperiments have bcen carried out on trapped particles. Those in
atomic physics (sec, for example, Richardson el ul., 1968) have been reviewed by Dehmelt
(1969) and by Wineland el ul. (1983).Those on microscopic particles include measurement of
light scattering by Straubel (1973)and by Blau a (11. (1970),of laser heating by Waniek and
Jarmuz (1968),of chemical reactions by Straubel(1982),of vapor pressure and gas transport
by Davis and Ray (1980) a ~ l dof conder~sationgrowth by Rubel (1981).
We report here the measurement of the deliquescence and subsequent evaporatior~and
recrystallization of single ammonium sulfate particles in electrodynamic suspension. A
charged solution droplet is injected into agtis-filled trap which is then evacuated to a pressure
of 10-"orr. Water vapor is slowly admitted to the trap until the (now solid) particle
deliquesces, then slowly removed until it recrysttlllizes. Particle relative mass and vapor
pressure are measured over the cycle which is repeated as required to insure reproducibility
and determine precision. This is the first use of high vacuum in the measurement of trapped
particle thermodynamics.
This work is part of a laboratory investigation of the dynamics of sulfate aerosols
sig~iificantin the atmosphere. In a closely related study Orr er a/. (1958)used an electrostatic
mobility chamber to measure the size of submicron aerosols, including ammonium sulfate, as
a function of relative humidity. Winkler and Junye (1972) used a delicate quartz liber
microbalance to measure the water absorption of natural and artificial aerosols with the
results analyzed by Winkler (1973).Tang rr al. (1977)used a flow reactor and light scattering
to measure the growth of sodium chloride particles by water absorption. The method was
also applied to ammonium bisulfate (Tang and Munkelwitz, 1977)and to mixed salts (Tang
et al., 1978). Recently Tang and Munkelwitz (1984)have used electrodynamic suspension of
sinkle particles to measure crystal nucleation in sodium chloride and ammonium sulfate
solutions.
vapor a t ambient t e m p e r a t u r e , i s momentarily h e a t e d w i t h IR
a t t a i n a new e q u i l i b r i u m due t o e v a p o r a t i o n . A t t h i s p o i n t t h e
so
C o n d e n s a t i o a l growth b e g i n s a t
is s l i g h t l y h i g h e r t h a n t h e a m b i e n t .
perature
the heat source is removed. Because of t h e h e a t r e l e a s e d by w a t e r vapor condroplet t e m p e r a t u r e d e c a y s r a t h e r s l o w l y , t h u s l i m i t i n g t h e d r o p l e t
theThe simultaneous
laass and h e a t t r a n s f e r p r o c e s s e s a r e f o r m u l a t e d f o r t h e
region, and a p r e s s u r e l i n e a r i z a t i o n p r o c e d u r e is i n t r o d u c e d t o r e d u c e t h e
lioear d i f f e r e n t i a l e q u a t i o n s t o a s y s t e m of f i r s t - o r d e r l i n e a r d i f f e r e n t i a l
yhlch are then s o l v e d a n a l y t i c a l l y f o r each s u c c e s s i v e time i n t e r v a l . Exten-
y l a l , . . m e ( L - P h e ) w a s investigat
ic p e p t i d e l i p i d s , N , N - , . J xade
~~~
d e a n d N. N - d ~ h e x a d e c ~ 6l _- ~ ~ ~
5His2C 16)
T h e coordination of
'L+ZC16 a n d L - P h e significantly
5 r a t e - d e t e r m i n i n g S t e p , convet
Se, w a s d r a s t i c a l l y accelerated.
s2C16, and t h e c o p p e r ( I 1 ) ion de
a m i n o a c i d s among nonenzymatic
the
.
dyaamic
p r o p e r t i e s of t h e aqueous s o l u t i o n s a r e used t o c a l c u l a t e e q u i l i b r i u m
pressures as a f u n c t i o n of d r o p l e t t e m p e r a t u r e and s o l u t e c o n c e n t r a t i o n . I t
amass accommodation c o e f f i c i e n t of u n i t y f o r w a t e r vapor c o n d e n s a t i o n on
'TIDES A N D P O L Y P E P T ~ D E ~
S ~ ~ YRIo c k e f e l l e r University,
droplets
g i v e s t h e b e s t agreement of t h e c a l c u l a t e d d r o p l e t growth w i t h
en synthesized whlch are capable to
and thus mlmlc blologlcal a c ( l ~ , ft o~
"REMENT OF PHASE CHANGES I N L i I.nH 0 . C. B. Richardson, C. A. K u r t z , P h y s i c s
y n i v = r s i t y o f Arkansas, ~ a g e t t e v i l l e , Arkansas 72701
Drwrtm,t
,d-soljd, 501 i d - 1 i q u i d , and 1 i q u i d - s o l i d phase changes a r e produced i n a l e v i croscoPic l i t h i u m i o d i d e p a r t i c l e a t room temperature b y v a r y i n g t h e pressure o f
ing
water vapor. F i v e c r y s t a l l i n e phases w i t h c o m p o s i t i o n L i I - n H 0, n = 0, 1,
3 are detected g r a v i m e t r i c a l l y , t h e n = 5 / 3 f o r t h e f i r s t time. i a t e r vapor
The h y s t e r e s i s d e t e c t e d i s evidence o f nucleaes are measured a t t h e t r a n s i t i o n s .
themdynamic
f l u c t u a t i o n s which w i l l be discussed. Water i n excess o f t h a t i n
ed s o l u t i o n i s absorbed i n t h e s o l i d - l i q u i d phase change, suggesting t h e f o r m a t i o n
tnterca1ation compound. The l i q u i d - s o l i d phase change i s f r o m a s u p e r s a t u=r a t e d
composition N
[H O j / [ L i I ] = 0.81 t 0.07 and w a t e r a c t i v i t y a
On
10The r e s u l t s w i l l be c6mpared w i t h t h e o r i e s o f e l e c t r o l y t e s a t higA concen-
MICAL P H Y S I C S OF A E R O C O L L ~ ~ ~ ~
'residing
ISTICS AN0 APPLICATIONS IN TRANSPOR~
c a l Engineering, U n i v e r s i t y of
.
t h e electrodynamic balance used for
o f a charged p a r t i c l e i n t h e
odes i s analyzed by s o l v i n g t h e
s o l u t i o n f o r t h e e l e c t r i c f i e l d to
c h a r a c t e r i s t i c s p r o v i d e a method for
Other methods O f drag f o r c e measur
asurements O f t h e drag f o r c e on
t'
se of t h e electrodynamic balance
SOLUTION DROPLETS USING
OPTICAL
Department, U n i v e r s i t y O F Arkansas,
Department of Applied Science,
1973.
I t h e growth r a t e of a s i n g l e s o l u t i o n
:edly measured v i t h h i g h p r e c i s i o n .
e q u i l i b r i u m w i t h w a t e r vapor a t aabient
1 0 um s o a s t o c a u s e a s h i f t i n
1R i r r a d i a t i o n is s u b s e q u e n t l y turned
il e q u i l i b r i u m s t a t e t h r o u e h coolinn aad
re r e p e a t e d s e v e r a l t i m e s Tor a given
r o p l e t s i z e a s a f u n c t i o n of time is
i t u n a b l e dye l a s e r .
A convenient
, a = 2nr/X, is u s u a l l y s e l e c t e d t o
?d w a v e l e n g t h , 1, of t h e probing lamer.
M t h a m a t h e m a t i c a l model t a k i n g i n t o
P r o c e s s e s i n t h e t r a n s i t i o n regime. A
led from t h e p r e s e n t Work f o r water
-
IN DROPLET NEAR EQUILIBRIUM WITH
to
WATER
lent of Applied S c i e n c e , Brookhaven
l e n s a t i o n a l growth of a s a l i n e droplet
l l e t , o r i g i n a l l y i n thermodynamic equi-
-
INVESTIGATION OF THE REACTION BEWEEN SINGLE AEROSOL ACID DROPLETS AND AMMONIA GAS
G.o. Kubel, Chemical R e s e a r c h and Development C e n t e r , A.P ,ti., MD. 21 01 0 a n d J . W .
ry, U n i v e r s i t y of Maryland, C o l l e g e P a r k , MD, 20783,
An experimental t e c h n i q u e has been d e v e l o p e d f o r t h e c o n t i n u o u s measurement of t h e
r w e t i o n dynamics between s i n g l e l i q u i d d r o p l e t s and r e a c t i v e g a s e s . The t e c h n i q u e i s
bled on t h e s u s p e n s i o n of e l e c t r i c a l l y c h a r g e d d r o p l e t s i n a n e l e c t r o d y n a m i c f i e l d where
droplet masses a r e d e t e r m i n e d from w e i g h t b a l a n c i n g d i r e c t c u r r e n t v o l t a g e s , From t h e
droplet mass h i s t o r y t h e e x t e n t o f r e a c t i o n i s d e t e r m i n e d a s a f u n c t i o n of t i m e , p a r t i c l e
.fie and ammonia g a s c o n c e n t r a t i o n . I t i s found s u r f a c e p h a s e r e a c t i o n , g a s p h a s e d i f f union and i n t e r n a l p a r t i c l e d i f f u s i o n s e q u e n t i a l l y c o n t r o l t h e p a r t i c l e r e a c t i o n dynamics,
The t r a n s i s t i o n from g a s p h a s e d i f f m s i o n t o i n t e r n a l p a r t i c ~ l ed i f f u s i o n c o n t r o l l e d r e r c tione i s i n i t i a t e d by p a r t i c l e c r y s t a l l i z a t i o n . The t i m e of c r y s t a l l i z a t i o n d e c r e a s e s
with i n c r e a s i n g ammonia g a s p r e s s u r e and d e c r e a s i n g p a r t i c l e s i z e . S u r f a c e s a t u r a t i o n s
of ammonium phosphate a r e c a l c u l a t e d from i n t e r n a l p a r t i c l e d i f f u s i o n models f o r t i m e s
Corresponding t o p a r t i c l e c r y s t a l l i z a t i o n a s a f u n c t i o n o l p a r t i c l e s i z e and ammonia g a s
pressure.
160.
THE APPLICATION OF AN ELECTRODYNAMIC BALANCE FOR MEASURING HETEROGENEOUS KINETICS
AT HIGH TEMPERATURES. R.E. S p j u t , Dept. o f Chem. Eng., M.I.T., Cambridge, MA 02139
A l s o , J . P . L o n g w e l l a n d A. F. Sarofirn
The e l e c t r o d y n a m i c b a l a n c e which h a s been s u c c e s s f u l l y used t o f o l l o w slow r a t e s o f
a s 8 change o f s i n g l e p a r t i c l e s a t c l o s e t o ambient t e m p e r a t u r e s h a s been m o d i f i e d f o r
i n s t u d y i n g f a s t r e a c t i o n s a t e l e v a t e d t e m p e r a t u r e s . A p a r t i c l e t y p i c a l l y 10-60 urn
in diameter i s suspended in t h e q u a d r u p o l e and h e a t e d by a f o c u s e d COZ-laser t o temperatures UP t o 4000 K. The t r a n s i e n t h e a t i n g r a t e d e p e n d s upon t h e power i n p u t and t h e
Particle s i z e b u t i s under a m i l l i s e c o n d f o r most p r a c t i c a l p u r p o s e s . The p a r t i c l e
t q e r a t u r e i s measured above 600 K by u s e
3-color pyrometry using l i q u i d - n i t r o g e n W l e d d e t e c t o r s w i t h e f f e c t i v e w a v e l e n g t h s o f 2 pm, 4 urn, and 4.8 um. A s e r v o - s y s t e m w i t h
a
time of 10 m i l l i s e c o n d h a s been i n s t a l l e d t o ~ e r m i tc o n t i n u o u s w e i g h t measure'nts.
Examples of a p p l i c a t i o n of t h e e l e c t r o d y n a m i c b a l a n c e f o r t h e measurement o f
"tes
v a p o r i z a t i o n r e f r a c t o r y o x i d e s and d e c o m p o s i t i o n o f l i m e s t o n e a r e p r o v i d e d .
6615
J . Am. Chem. Soc. 1984, 106, 66 15-66 18
from the most stable Pt, cluster by addition of a single Pt atom
to the unmodified compact Pt, structure. This would imply the
formation of an outgrowth which, except for the structure (8,21),
cannot generate a structure with large spherical density. A significant reorganization is required to restore the compactness. In
a similar way, the low-density surface of a crystal restructures
relative to the crystal bulk. The number of MIDs is a good index
number of the stability of the clusters of class A. Indeed, all its
most stable clusters have the largest number of MIDs at the EHT
level. This property is also true at the EHT-SO level except for
the structures (11,l) and (12,1), which come after (11,2) and
(12,2) while they have one MID less. These exceptions have been
explained by the small geometrical constraints existing for bilayer
clusters and by the sp populations.
When structures of class C are considered, the MID index
number is only a helpful indication of the stability at the EHT
level since some structures of class C have the largest cohesive
energies without having the maximum number of MIDs. These
structures have a large spherical density. Structures (8,24),
(10,35), and (12,6) illustrate this point. As their SO contribution
is weak, structures with the maximum number of MIDs ((8.21)
from class C and (10,l) and (12.2) from class A) reappear as the
most stable isomers at the EHT + S O level.
Since structures of class C are not suitable for an extension
toward an infinite crystal and their cohesive energies are lower
than for those of the fcc or hcp bulk, compounds of class A or
B should prevail for the medium or large clusters. With such a
growth, the mean number of MID per atom can converge to 6,
the value for the bulk. For the small systems, the occurrence of
some fragments of fcc or hcp type (Pt,, Pt4, Pt,, Ptq, Ptlo, Ptll,
Pt,,, and Pt,3) in the growth at the EHT S O level 1s due more
to their own compactness than to their classification as clusters
of class A.
The EHT and EHT + S O methods are more selective than the
simple Lennard-Jones interactions. For example, one Pt,,
structure clearly emerges as the most stable within the EHT +
S O framework while 987 structures are quasi-degenerate within
a Lennard-Jones analy~is.'~
The present results will be used to study the hydrogenation
process of the Pt, clusters.
+
Acknowledgment. This work has been supported by an ATP
surface grant from the CNRS. We are pleased to thank Professor
Fraissard for many discussions on the existence and the properties
of small particles of platinum. We are grateful to Dr. Spanjaard
for stimulating discussions on spin-orbit influence.
Reglstry No. Pt. 7440-06-4.
A Novel Isopiestic Measurement of Water Activity in
Concentrated and Supersaturated Lithium Halide Solutions
C . B. Richardson* and C.A. Kurtz
Contribution from rhe Physics Deparrmenr, Uniuersify of Arkansas.
Fayetteuille, Arkansas 72701. Received May 2, 1984
Abstract: In a variation of the Stokes bithermal isopiestic method, single microscopic drops of lithium bromide and lithium
iodide aquenus solution at room temperature are levitated electrodynamically in a closed chamber from which air is removed
and Lo which is connected a vial of pure water at lower temperature. Water temperature is varied between -74 and +21 "C
to measure concentrated and supersaturated solution water activity from 4.5 X lo-' to 0.9. The results are compared with
those of regular solution theory and the adsorption and stepped-hydration theories of Robinson and Stokes.
The isopicstic method for the determination of water activities
in salt solutions is simple, precise, and general. Known amounts
d containers in an isothermal
of nonvolatile solutes are ~ k ~ ine oDen
enclosure into which water is intioduced. At equilibrium the
solution water activities are equal and the compositions are determined by weighing. With activities of reference solutions, e.g.,
NaCI, KCI, H2S04,and CaCI2, determined by vapor pressure and
other measurements, the comparison method has yielded activities
a, of hundreds of solutions over wide rangcs of concentrations and
temperatures.' With temperatures fixed to 10.05 K or better,
temperature differences between samples less than lo4 K, and
mass measurements precise to f0.05%, the method yields composition ratios with a precision greater than lo4 and ultimately,
osmotic coefficients 4 = -(N/v) In a, with a precision greater than
lo-'. Here N = IH20]/[X] is the solvent-solute and v the ionsolute molar ratio.
A lower bound on a, is placed by the crystallization of the
reference, e.g., al 2 0.753 for NaCl a t 25 'C. In a variation on
the method which avoids the lower bound, Stoke:' replaced the
solution reference with pure water at reduced ten,:rature. He
obtained good agreement with other measurements but did not
(1)
Robinson. R. A.; Stokca, R.H., YElectrolyte Solutions"; Butterworths;
London. 1959.
(2) Stokes, R. H . J. Am. Chem. Soc. 1947, 69, 1291.
0002-7863/84/1506-6615%01.50/0
push a, below 0.2889. A second lower bound is placed by crystallization of the unknown of course. Though many of the compounds listed in ref 1 have been measured to saturated solution,
we know of no listings there for supersaturated solutions. Ionic
solutions at the high concentrations of supersaturation may become
ordered liquids for which water activity can serve as a probe.
We report here the results of an isopiestic study of lithium
bromide and lithium iodide solutions by the Stokes method in
Our method
which water activity is measured down to 4 X
differs in the handling of the sample. We have reduced its mass
to
g, compared with the 1 g typical of isopiestic samples, have
levitated it electrodynamically in a small sealed chamber from
which air is removed, and have weighed it in situ and continuously
with a noncontacting electrostatic balance.
With a microscopic spherical sample in a small chamber containing only water vapor, equilibrium is established much faster.
More importantly, levitation of microscopic droplets allows supersaturation terminated only by homogeneous nucleation of
crystallization.
We apply regular solution theory? adsorption model t h e ~ r y , ~
and stepped-hydration model theory5 to our results.
(3) Pitzer, K. S . Ber. Bunsmges. Phys Chem. 1981, 85, 952,
(41 Stokes, R. H.:Robinson, R, A. J. Am. Chem, Sac. 1948, 70, 1870,
( 5 ) Stokes. R. H.; Robinson, R. A. I . Soln. Chem. 1973. 2. 173.
Q 1984 American Chemical Society
1a1
.
Aerosol Science and Technology, v 2, Issue 2, p 184-184, 1983
INVESTIGATION OF AHl.!ONIUl,! SULFATE AEROSOLS
USING 'ELECTRODYNAt.!IC SUSPENSION, C. 6.
Richardson, J. F. Spann, C. A. Kurtz,
Physics Department, Universl t y of
2N3
Arkansas, F a y e t t e v i l l e , AR 72701
-
A l a b o r a t o r y study o f s u l f a t e aerosols
i s i n progress. Single, micron-size,
ammonium s u l f a t e p a r t i c l e s a r e suspended
i n a quadrupole i o n t r a p i n t o which are
introduced r e a c t i v e gases. P a r t i c l e
growth i s monitored o p t i c a l l y , aerodynami c a l l y , and by using t h e t r a p as a mass
spectrometer;
The t r a p i s constructed o f s t a i n l e s s
s t e e l and n i c k e l mesh. I t has a height o f
12 mm and a diameter of 20 mn. Voltages
between 100 and 1000 are applied a t a f r e quench o f 200 Hz.. The t r a p i s mounted i n
a glass and s t a i n l e s s s t e e l chamber connected t o a manifold through a p r e c i s i o n
leak valve. Gases f i l l t h e manifold
through bakeable stopcocks. The system i s
evacuated by a turbomolecular pump. With
m i l d bakeout a base pressure o f lom6 t o r r
i s q u i c k l y obtained. Pressures a r e measured wi t h c o l d cathode and thermocouple
gauges and a capacitance manometer.
P a r t i a l pressures a r e measured w i t h a
quadrupole r e s i d u a l gas analyzer and a
humidi t y - s e n s i t i v e transducer.
P a r t i c l e s i n s o l u t i o n phase are projected i n t o t h e t r a p through t h e mesh.
They a r e charged i n d u c t i v e l y , e i t h e r posit i v e o r negative, a t any value desired up
t o t h e Rayleigh l i m i t . When trapped,
t h e i r p o s i t i o n i s f i x e d w i t h i n about 2
microns except a t high vacuum when small
o s c i l l a t i o n s occur. Trapping times are
unlimited.
V e r t i c a l l y p o l a r i z e d l i g h t from a
helium-neon l a s e r i s scattered from t h e
p a r t i c l e and detected v i s u a l l y and photoe l e c t r i c a l l y b y two p h o t o m u l t i p l i e r tubes,
mspheric-
one f i x e d a t 90' i n t h e horizontal plane,
the other moveable. Mie theory I s f i t to
the scattered l i g h t r e s u l t s t o obtain part i c l e radius and r e f r a c t i v e index.
Gravity i s balanced by a v e r t i c a l f i e l d to
determine r e l a t i v e mass w i t h a precision
o f about 2 x 10-3. The p a r t i c l e motion is
resonantly d r i v e n t o measure damplng and
determine surface area.
The response of t h e P a r t i c l e t o changi n g pressure o f water vapor has been
measured. The r e s u l t s include t h e following.
a) At ambient temperature T = 23.5O c
the t r a n s i t i o n from anhydrous (NH ) SO
occurs a t water pressure P = 18.04f20.$
t o r r . The s o l u t i o n composition i s 44.4 +
0.3% ammonium s u l f a t e . These values are
i n good agreement w i t h the T = 25" C values
o f Robinson and Stokes: 18.9 t o r r , and
44.2%.
b) During t h e t r a n s i t i o n , when the
p a r t i c l e I s layered, H i e s c a t t e r i n g a t 9D0
i s detected. Regular o s c i l l a t i o n s i n i n t e n s i t y are recorded.
c ) During growth o f the l i q u i d p a r t i c l e t h e scattered l i g h t passes through intense van de H u l s t resonances whose widths
correspond t o mono1ayer addition.
d) Growth i s reversed and t h e vapor
pressure o f t h e supersaturated s o l u t i o n i s
measured. A t t h e p o i n t o f t r a n s i t i o n t o
0.9 t o r r when t h e composolid, P = 10.8
s i t i o n i s 72.3 f 0.7% amnonium sulfate.
e) The t r a p i s evacuated and t h e an3
hydrous p a r t i c l e i s held a t P * 3 x 10t o r r f o r 48 hours. An upper l i m i t on the
evaporation r a t e y i e l d s upper l i m i t s on
t h e vapor p r e s s u r e ~ ~ os fu l f u r i c t 6 i d and
a m n i a o f 2 x 10and 6 x 10torr,
respectively.
+
This work i s supported by NSF Grant
ATk1 8202766.
I
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L I ~ mSCATTERI:
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The chart
sized particl'
both the part.
the light sca'
described.
can b e
scattering i n
~ ~ e l l ewrt r i
and related t
the scatterel
meters.
Three PE
geometrical 6
to an equal \
These include
cribe the tw<
function of
meter that d
geometrical
resistance i
shape factor
is the r a t i o
given par t i c
the resistar
experiences
dynamic shal
while that 1
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dynamic sha:
axial r a t i o
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*
.CHEMICAL PHYSICS LMTERS
MICROSCOPIC LITHIUM IODIDE PARTIC
fre~~ille.
Arknnsus 72701, USA
ject of a large number of studies usi
techniques. The>continuinginterest ma
barriers. The transition from crystal to saturated solution is time resolved with the results suggesting the
presence of an intermediate disordered solid, possibly
an intercalation compound. The supersaturated solu-
s are derived from reducing the sameparture of the system
limination of solid contact
t removes a source of
forms n = 112 [I] and n = 312 [4]
but not confirmed.'Lithium iodide
good solid electrolyte [5]. The hig
is consistent with the known disorder
positions in the crystal. Thermogravi
pressure measurements have been u
the phase diagram of the solid sy
sured [R].
Where possible we compare our res
ones, and offer explanations where si
agreement is found.
The quadrupole ion trap by w
levitated is simiir to that used by
en the sub-
description of the system is given
0 009-2614/84/$03.00 O Elsevier Sc
(North-Holland Physics Publishing Di
3
HI7
P r o p e r t i e s of He Adsorbed on Graphite Derived from
S c a t t e r i n Data. W . E. CARLOS and u. W. COLE, Penn S t a t e
U.--With :ata f o r ' ~ eand 'He s c a t t e r i n g from graphite
as
i n p u t , we d e r i v e the atom-surface i n t e r a c t i o n i n t e r n of
a s~lmmationof tie-C p a i r p o t e n t i a l s (6-12, ~ u k - 6 , e ~ ~ - 6 ) ~ .
The a n i s t r o-w- of the p a i r i n t e r a c t i o n i s taken i n t o account t o obtain a good f i t t o the matrix elements. The
imdel p o t e n t i a l is t h e n used t o c a l c u l a t e the band s t r u c t u r e of He on g r a p h i t e . By including t h e e f f e c t s of band
s t r u c t u r e and adatom-adatan i n t e r a c t i o n s , we f i n d t h e
ground s t a t e energy of helium on graphite derived from
thermodynamics agrees t o w i t h i n one per cent of t h a t
derived frcm s c a t t e r i n g f o r both He isotopes. We a l s o use
t h e nude1 p o t e n t i a l t o c a l c u l a t e o t h e r thermodynamic prop e r t i e s of He films on g r a p h i t e a t l w coverage.
IG. Boato, P. C a n t i n i , and R..Tatarek, Phys. Rev. L e t t .
40. 887 (1978) and Surf. S c i . , t o be published; G. Derry
e t a l . , p r i v a t e comnunication.
2 ~ .E. Carlos and H. W . Cole, Surf. S c i . 77, L173 (1978).
3 ~ .L. Elgin, J . U. G r e i f , and D. L. Goadzein,
submitted
t o Phys. Rev. L e t t .
HI 3
Photon Excitation of Compound Plasmon Resonances i n
Aluminum. C.
8. RICHARDSON AND- 8- . U. H. MCLEAN.
.~
-.
Universit of Arkansas.--Modulated aluminum surfaces
were grod;ced by t h e superposition of two rulings of
8980 A soacina.
disolaced
s l i a h t l v i n a n ~ l e . Surface
a m - - piiimons a r e excited by l i g h t - a t i328 b e l e n g t h
incident i n a plane perpendicular o r parallel t o t h e
angle b i s e c t o r . Resonant processes up t o sixth-order
i n the photon-plasmon-grating i n t e r a c t i o n a r e required
t o y i e l d the d i f f r a c t i o n observed. For a g r a t i n g with
2" between the r u l i n g s and para1 l e l incidence, the
r e l a t i v e i n t e n s i t y of l i g h t produced by the s i x t h - o r d e r
and second-order processes i s 4 x 10-4. These and
s i m i l a r r e s u l t s w i l l be compared with a quantum theory
of intermediate plasmn-photon resonant s t a t e s .
- r - -
HI 4
Plasmon L o s s i n P h o t o e l e c t r o n , Auger a n d
EEL
S ~-c- c- -t r aof
TROOSTER a n d
-- - - -A1
- - and
-..- Ma.* JAN M.
PAUL M. VAN * ~ ~ ~ ~ , ~ - ; j a r t r n oef n M
t olecular
S p e ~ t r ~ s c ~ pU n
y i,v .
N egen, Netherlands.-T h e i n t e -n s- -i -t- i e- x ~ l a s m zl o s s s a t e l l i t e s o f
core l i n e s a n d v a l e n c e b a n d i n t h e x - r a y p h o t o electron
a n d A u g e r s p e c t r a o f A1 a n d Mg w e r e
d e t e r m i n e d b y c o n v o l u t i n g the n o - l o s s s p e c t r a
w i t h asymmetric L o r e n t z i a n s .
I n both metala
t h e i n t r i n s i c p l a s m o n loss i n t e n s i t y i s 25% o f
Extrinsic
t h e t o t a l p l a s m o n loss i n t e n s i t y .
plasmon l o s s i n t e n s i t y was d e t e r m i n e d independe n t l y from e l e c t r o n energy l o s s s p e c t r a .
Plasmon g a i n s a t e l l i t e s w e r e o b s e r v e d i n t h e
KLL-Auger s p e c t r a , c o n f i r m i n g t h e i m p o r t a n c e
o f t h e i n t r i n s i c plasmon l o s s e s .
~~
~
of
S e l e c t i v e Adsorption of * ~ and
e ' ~ eon t h e Basal
HI 8
Plane of Gra h l t e . 4 G . Derry, D. Wesner, and D. R.
Frankl, PennPState 0.4.--Atomc
beams of * ~ and
e ' ~ ewere
r e f l e c t e d f r a n b a s a l p l a n e s u r f a c e s of n a t u r a l g r a p h i t e
s i n g l e c r y s t a l s i n u l t r a h i g h vacuum. The bound s t a t e
eigenvalue s p e c t r a of both i s o t o p e s were i n f e r r e d from
t h e s e l e c t i v e adsorption minima i n t h e r e f l e c t e d intens i t y . The r e s u l t s a r e E, = 12.06 t 0.13 meV, E l = 6.36
t 0.11 meV, E2 = 2.85 -+ 0.10 mev, E3 = 1.01 f 0.09 meV,
and E, = 0.17 f 0.06 meV f o r 'He on g r a p h i t e , and E, =
11.59 ? 0.08 meV, E , = 5.36 f 0.15 meV, and E2 = 1.78 t
0.11 meV f o r ' ~ eon g r a p h i t e . These data were obtained
on two c r y s t a l s , and measurements on a t h i r d c r y s t a l a r e
i n progress. .The energy l e v e l values obtained f o r 'He
adsorption a r e c l o s e t o , b u t s l i g h t l y deeper than those
obtained by Boato e t a l . ' and agree well with a n a l y s i s
of thermodynamic d a t a .
*Submitted by D. R. FRANKL.
**Supported by N.S.F. Grant No. D m 77-229Qand by the
Applied Research Laboratory of Penn S t a t e University.
'G. Boato, P. C a n t i n i , and R. Tatarek, Phys. Rev. L e t t .
40, 887 (1978).
Tii. L. Elgin. J. M. G r e i f , and D. L. Goodstein. submitted t o Phys. Rev. L e t t .
-
* S u b m i t t e d b y N. B e n c z e r - K o l l e r .
HI 5
Photoelectron I n j e c t i o n i n Gases from Thin Metal
Films on guartz.* K. SIOMOS and L.G. CHRISTOPHOROU,
Ridge National Laboratory--The photoelectron i n j e c t i o n
current (PEIC) i n gases from t h i n metal films of Pd. Au.
and Au + Pd on quartz was measured a s a function of film
thickness, film homogeneity, gas pressure, pressucereduced e l e c t r i c f i e l d and photocathode m a t e r i a l conditioning. The PEIC v a r i e s with f i l m composition and
thickness. I t i n c r e a s e s almost exponentially witho
decreasing f i l m thicknegs i n t h e range -30 t o 400 A, but
i t decreases below 230 A.
These r e s u l t s w i l l be d i s cussed, and t h e i r relevance t o s t u d i e s of the behavior of
excess e l e c t r o n s i n f l u i d s , vhere optimum PEICs a r e
required, w i l l be indicated.
HID
Magnetoplasma P o l a r i t o n s a t
I n t e r f a c e Between a Semiconductor
M e t a l l i c Screen.P.HALEV1,
4 8 , P u e b l a . P u e . H 6 x i c o a n d C.GUERRA-VELA
*Research sponsored by the Division of Biomedical and
u r d u e U.-An i n t e r f a c e b e t w e e n a s e m i Environmental Research, U.S. Department of Energy under
k
r and a h i g h l y conducting metallic
c o n t r a c t W-7405-eng-26 with Union Carbide Corporation.
s c r e e n s u p p o r t s p o l a r i t o n s which propagat e a t a r i g h t a n g l e t o a s t a t i c magnetic
HI 6
f i e l d lying i n the plane of the i n t e r f a c e
w u m ~wmnm enennru. w o ~ o ~ ~ e c r nwen
rc
( ~ P E )m
(Voigt geometry). I n c a s e of n e g l i g i b l e TETUCEME. S. Arnold (Polytachnic I n a t i t u t 8 o f 3 - d
M.
plasmon-phonon i n t e r a c t i o n t h e r e is a p r o
Pope (RN). I n 1965 Popm a t aL obaerrad 8 DQEPE in cry.p a g a t i o n window b e l o w t h e c y c l o t r o n f r e t a l l i n e tmtracme. f h i 8 proem88 conmiat8 of t h e emi88i00
quency and a n o t h e r one above t h e h y b r i d
of photomlmctrona Under thm aCtiOU of l i g h t of mnmrgy much c y c l o t r o n p l a s m a f r e q u e n c y . F o r a g i v e n
below t h r t of t h e e x t m m l ionismtion thre8hold of th8
o r i e n t a t i o n o f the magnetic f i e l d these
crymtal. Ihm p h o t o d a m i o n rat. varied a 8 th8 8quar8 of
modes p r o p a g a t e i n o p p o s i t e d i r e c t i o n s .
t h e l i g h t t t s n 8 i t y I. with the u u r g y of th. m a t mnmrget- I n c a s e o f a p o l a r s e m i c o n d u c t o r t h e r e
i c mlectron unaffected by photon energy i n t h i 8 low energy a r e t h r e e p r o p a g a t i o n windows whose
region. They attributmd t h e DQEPE t o t h e i n t e r a c t i o n of
l i m i t i n g f r e q u e n c i e s depend on t h e
c y c l o t r o n , plasma, t r a n s v e r s e phonon, and
tvo h i t h e r t o m d 8 t a c t e d c h r g e - t r a n 8 f 8 r (CT) a c i t o n
?hi8 conclu8ion ram c h l l l r ~ e dby &.arm1 a d C.8tro."who
l o n g i t u d i n a l phonon f r e q u e n c i e s . T h e s e
f a i l e d t o obaem8 any
EPE a t a11 in tetracane. Iha exmodes a l s o e x h i b i t n o n r e c i p r o c a l i t y w i t h
p e r L e n t of Popm e t 81PQlaem bmen r e p u t e d uaiag more manrespect t o t h e i r direction of propagation
a i t i v a aqui-t
=cfopad
by ~ r n o l d . N.v
~
rmaultm v e r i f y E f f e c t s o f d a m p i n g , o f t h e f i n i t e c o n d u c t i v i t y o f t h e m e t a l l i c s c r e e n , and t h e
t h 8 e x i s t e n c e of
DQKPE. The p h o t o a d . i o n r a t e i a
p o s s i b i l i t y of experimental d e t e c t i o n of
proportional t o 15)' and t h e proc8'8 i 8 ind8pmdent of
Photon m e r a y o r 8inglmt u c i t o n concentration. An anert h e p r e d i c t e d modes a r e d i s c u s s e d .
g a t i c a l l y and k i n e t i c a l l y r u 8 0 ~ b l eh~wothe8iaInvolve8
tbm i n t e r a c t i o n of a f r e i conduction 8 i i c t r o n with a
HI 1 0 Build Up of Reflected Signal i n Time from a
trapped CT u c i t o n .
Frequency and S p a t i a l l y Dispersive Medim.* D.N. PAlTANAYAK and J.L. BIFNAN. CCNY-N.Y. 10031--We consider the
1. U. Pop8 e t d., J. Chm. Phy.., 41, 3367 (1965).
problem of r e f l e c t i o n o f a Heavyside Sinusoidal s i g n a l
2 . D. b w n . C r i t . h v . Sol. S t a t . Sci.. 3, 243 (1973).
The
from a S p a t i a l l y Dispersive D i e l e c t r i c Half-Specr.
3. S. Arnold, t o bc publi#h8d.
build up of t b e r e f l e c t e d s i g n a l t o i t s asymptotic
a
-
-
--
--
steady s t a
coupled po
mass motio
ref l e c t i v i
(1) D. Ele
up ported
PSC-BHE 1:
HI 11Interface E
BIRHAN and
--We consid
dense'' eonreflected f
l o c a l mediu
----"- "-"
,,"YSllP
La11
i n the loca
medium i s a
obeying a s
c r i t i c a l arq
occur: selet
l a t e r a l disl
energy red11
w i l l be givt
study o f sur
(1) B.R. Hol
L.H. Brs
Supported b
PSC-BHE 122
;
,
f
HI 12
Grai
from D i e m
of Maine, Or
of water MI
Thus the re1
range and th
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I
JA4r
O R I C S COMMUNICATIONS
(w,, -,e shown in fig.
o fig. 1. Here v b o is
ncy. As well as giving a
is introduced.
kground noise manifest
on. This distortion o
it low frequencies in
unt of distortion dep
can only be determi
ctual calculation.
wer for his helpful corn
January 1979
pHO.ro~EXC[~,-ATION
OF COMPOUND PLASMON RESONANCES IN ALUMINUM
C,B.RICI-{,:\RDSONand B.W.11. k L E A N
pllysicr Dc r70,.
,,,(,,'
U n i l ! r r s i t ~ofArkansas.lhyetfeville, Arka~:sas72701. USA
~ 35 Scpte~nbtlr
~
1978
~
~
we
i
~
~
d
c,ujied the diffraction of light from aIuminum surfaces ruled in parallclogram patterns. Sharp intensity varia-
any as rllrce virtual plasmons in resonance.
2. Experiment
qlaining tlr? observed variations in the intenlight diffracted from aluminum and gold
s, Ritchie t't al. I l j presented a quantum theory
rnpound process in wluch a final photon state
s fro111 an intermediate surface plasmon state
1 plasn1011.The probability of excitation may
ntzian functii~nof the photon-plasmon enernce or. at a fixed photon energy, of the varienta tralisferred. The sharply peaked variathe diffracted light intensity indicate narrow
resonances in the 0.3 to 1.3 pm wavelength
The gratings were prepared holographically using
photoresist on glass plates and a fringe pattern formed
by splitting the beam of on argon-ion laser tuned t o
0.4579 pm. They were made in the form of grids by
rotating the plates in their planes through an angle 0
to a depth of roughly 0.1 pm. From diffraction, the
grating spacing d was found to be 0.898 5 0.005 pm
and the modulation amplitude h was found. [2] to be between 0.014pm and 0.03Opm for the gratings studied.
The gratings were mounted in a two-axis goniometer and illuminated by unpolarized light at 0.6328
pm from a helium-neon laser. Diffracted light was detected by a 9502 B photomultiplier. A polarizer and
. In a fourtli-order process, for example, the
ate slate could include two virtual plasmons
irtllal plloton in resonance. The probability
tion of such a state would vary as the product
Fig. 1. Schematic representation of diffraction at
b, =
90'.
7
8 Kirk-Othrner, Encyclopedia of Chemical Teelrnology
(Interscience, New York, 1965), Vol. 8, 2nd ed., pp. 891.
In our experiment as we have determined the resonant
frequency to a better accuracy than the area of the coil
"A," exprdon ( 8 ) is used in preference to expression (3).
Also the values of K and other comtion terms due to the
finite radius of the wire and the pitch of the winding (see
Ref. 5, pp. 429-432) can be avoided for the determination
of p, as described in this paper.
F. Langford-Smith, Radio Designer's Handbook (Iliffe
Book Ltd., London, 1967),4th ed., pp. 430.
'
Measurement of the Speed of Light
A. J. DOMKOWSKI
C. B. RICHARDSON
Univerdy of Arkanam
Fayetiem%, Arkanma 78701
NOEL ROWBOTHAM
College of the Ozarks
Clarksvzlle, Arkansas
(Received 29 November 1971; revised 12 January 1972)
The measurement of the speed of light by the
rotating mirror method of Foucault is at once
beautiful in its simplicity, significant in its
content, and impressive in its outcome. With a
light source and detector, three mirrors, and a
lens students can, in effect, measure transit times
for light of lo4 sec over a path within a classroom
and, with the simple equipment we will describe,
to a precision of better than 1%.
The arrangement of these components, identical
M w r e m e n t of the speed of light by the rotaling
mirror method of Foucault wing a h e r source and to the original arrangement of Foucault, is
photodiode deledor is deadbed. With a path length of shown in Fig. 1. In 1850 Foucault obtained the
$8 m and rotation rates u p to 600 Hz, the result c=
result c=298 000f 500 km/sec. He and others,
3.00fO.08X 108 m/sec is obtained.
including Michelson, subsequently refined the
technique, principally through the introduction of
longer paths. Michelson's first result, given in
1879 was c=299 910f 50 km/sec, his last from
the measurements from Mt. Wilson in 1926 was
299 798f 4 km/sec.l
Light from the source L is reflected from the
rotating mirror M so that the beam is swept
through a large arc. Within that arc it strikes
normally a plane reflector R, returning from it to
the mirror M. Because M has rotated through an
angle 8 during the light's transit of MRM the
beam returns to the partially reflecting mirror S
along a path deviating 28 from the incident path.
At S it is reflected to the detector D which is
moveable perpendicular to the reflected beam.
The lens F having a focal length onefourth the
distance between L and R is placed midway
between them producing a sharp image of the
RQ.1. Arrangement of components in the rotating mirror source at R and at D. The procedure is to set the
method of Foucault. L, laser source; M, rotating mirror;
R, plane reflector;F, lens; focal length 4.75 m; S, partiaUy rotational frequency f of the mirror to various
values and for each to locate the position p of
silvered mirror; D, moveable photodiode detector.
910
/ June 197.9